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Contributions to the theory of group rings

  • Authors: Groenewald, Nicolas Johannes
  • Date: 1979
  • Subjects: Group rings Group theory -- Mathematics
  • Language: English
  • Type: Thesis , Doctoral , PhD
  • Identifier: vital:5391 , http://hdl.handle.net/10962/d1001980
  • Description: Chapter 1 is a short review of the main results in some areas of the theory of group rings. In the first half of Chapter 2 we determine the ideal theoretic structure of the group ring RG where G is the direct product of a finite Abelian group and an ordered group with R a completely primary ring. Our choice of rings and groups entails that the study centres mainly on zero divisor ideals of group rings and hence it contributes in a small way to the zero divisor problem. We show that if R is a completely primary ring, then there exists a one-one correspondence of the prime zero divisor ideals in RG and RG¯, G finite cyclic of order n. If R is a ring with the property α, β € R, then αβ = 0 implies βα = 0, and S is an ordered semigroup, we show that if ∑α¡s¡ ∈ RS is a divisor of zero, then the coefficients α¡ belong to a zero divisor ideal in R. The converse is proved in the case where R is a commutative Noetherian ring. These results are applied to give an account of the zero divisors in the group ring over the direct product of a finite Abelian group and an ordered group with coefficients in a completely primary ring. In the second half of Chapter 2 we determine the units of the group ring RG where R is not necessarily commutative and G is an ordered group. If R is a ring such that if α, β € R and αβ = 0, then βα = 0, and if G is an ordered group, then we show that ∑αg(subscript)g is a unit in RG if and only if there exists ∑βh(subscript)h in RG such that∑αg(subscript)βg(subscript)-1 = 1 and αg(subscriptβh is nilpotent whenever GH≠1. We also show that if R is a ring with no nilpotent elements ≠0 and no idempotents ≠0,1, then RG has only trivial units. In this chapter we also consider strongly prime rings. We prove that RG is strongly prime if R is strongly prime and G is an unique product (u.p.) group. If H ⊲ G such that G/H is right ordered, then it is shown that RG is strongly prime if RH is strongly prime. In Chapter 3 results are derived to indicate the relations between certain classes of ideals in R and RG. If δ is a property of ideals defined for ideals in R and RG, then the "going up" condition holds for δ-ideals if Q being a δ-ideal in R implies that QG is a δ-ideal in RG. The "going down" condition is satisfied if P being a δ-ideal in RG implies that P∩ R is a δ-ideal in R. We proved that the "going up" and "going down" conditions are satisfied for prime ideals, ℓ-prime ideals, q-semiprime ideals and strongly prime ideals. These results are then applied to obtain certain relations between different radicals of the ring R and the group ring (semigroup ring) RG (RS). Similarly, results about the relation between the ideals and the radicals of the group rings RH and RG, where H is a central subgroup of G, are obtained. For the upper nil radical we prove that ⋃(RG) (RH) ⊆ RG, H a central subgroup of G, if G/H is an ordered group . If S is an ordered semigroup, however, then ⋃(RS) ⊆ ⋃(R)S for any ring R. In Chapter 4 we determine relations between various radicals in certain classes of group rings. In Section 4.3, as an extension of a result of Tan, we prove that P(R)G = P(RG) , R a ring with identity , if and only if the order of no finite normal subgroup of G is a zero divisor in R/P(R). If R is any ring with identity and H a normal subgroup of G such that G/H is an ordered group, we show that ⊓(RH)·RG = ⋃(RG) = ⊓(RG) , if ⋃(RH) is nilpotent. Similar results are obtained for the semigroup ring RS, S ordered. It is also shown if R is commutative and G finite of order n, then J(R)G = J(RG) if and only if n is not a zero divisor in R/J(R), J(R) being the Jacobson radical of R. For the Brown HcCoy radical we determine the following: If R is Brown McCoy semisimple or if R is a simple ring with identity, then B(RG) = (0), where G is a finitely generated torsion free Abelian group. In the last section we determine further relations between some of the previously defined radicals, in particular between P(R), U(R) and J(R). Among other results, the following relations between the abovementioned radicals are obtained: U(RS) = U(R)S = P(RS) = J(RS) where R is a left Goldie ring and S an ordered semigroup with unity
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  • Date Issued: 1979

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Gloria

Gloria

Nkosi sikelela

Dispersal of the cochineal insect Dactylopius Austrinus de Lotto (Homoptera : Dactylopiidae)

  • Authors: Gunn, Brian Howard
  • Date: 1979
  • Subjects: Cochineal insect--South Africa , Cochineal insects , Biological control , Jointed cactus , South Africa
  • Language: English
  • Type: Thesis , Doctoral , PhD
  • Identifier: vital:5596 , http://hdl.handle.net/10962/d1002046
  • Description: Dispersal of the cochineal insect Dactylopius austrinus De Lotto, introduced into South Africa in 1932 as a biological control agent against jointed cactus Opuntia aurantiaca Lindley, was investigated. Zimmermann et al. (l974) suggested that the apparent failure of this insect to control jointed cactus infestations is due to limited dispersal of the first instar nymphs (hereafter referred to as crawlers). Studies on crawler morphology have shown a clear sexual dimorphism in the pattern and development of filaments on the head, thorax and abdomen of male and female crawlers. This enabled differentiation between the sexes with respect to terminal velocities, behaviour and survival of crawlers which have shown that the crawlers, especially the females, are well adapted to dispersal. Long filaments on the head, thorax and abdomen of the female crawlers, that are restricted to dispersal in the crawler stage (as later instars are sessile) and a behaviour directed towards "take-off" enhance the potential for dispersal. The more sedentary males, with long filaments restricted to the abdomen, are able to disperse as winged adults. The principal factors influencing the timing of dispersal and number of crawlers blown from the host plant are wind and temperature; the latter determining the number of crawlers moving on the host plant. Dispersal is confined to the period between 06h00 and 20h00 and it was possible to correlate the pattern of crawler dispersal with wind patterns. The general equation of Taylor (1978) provided an adequate description of horizontal distribution of D.austrinus crawlers in all directions. Wind dispersal of the apterous crawlers is restricted by the low height of jointed cactus plants. Horizontal distribution is limited (generally less than 10 m) although a small proportion of crawlers carried vertically upwards by turbulence or convection currents are sufficiently hardy to survive long range displacement. It is suggested that the small size of the host plant will also reduce effective colonization as the canopy area provides a small target for the wind-blown crawlers. The limitation on dispersal due to the low height of the host plant suggested a system for artificially enhancing crawler dispersal from elevated towers in the field. Evaluation of this system confirmed that it would be practical to augment or introduce cochineal into jointed cactus infestations to enhance the biocontrol potential of this insect. This offers an alternative to chemical control, that has so far failed to control the spread of jointed cactus despite an intensive and expensive herbicide program
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  • Date Issued: 1979

The study of hydroxyoximes and hydroxamic acids supported on macroporous resins and their use in the rapid seperation of metals

  • Authors: Hemmes, Marlene
  • Date: 1979
  • Subjects: Chromatographic analysis , Separation (Technology) , Metal ions , Solvent extraction , Extraction (Chemistry) , Oximes , Metals -- Analysis
  • Language: English
  • Type: Thesis , Masters , MSc
  • Identifier: vital:4453 , http://hdl.handle.net/10962/d1009512
  • Description: Introduction: The macroporous Amberlite XAD resins were coated with LIX-64N and examined for the rate of uptake of copper . XAD-7 was by far the best support and gave a satisfactory rate of uptake up to loadings of 60% (w/w). The specific surface area of XAD-7 was measured by the adsorption of methylene blue from aqueous solution. The area of the wetted resin was five times less than that of the dry resin. LIX-65N was purified and the anti isomer characterised using spectroscopic techniques . The rate of uptake of copper was not improved by use of purified LIX-65N or by addition of LIX-63. XAD-7 coated with LIX-65N was used in columns. Elution curves for copper showed negligible tailing, and rapid separations of copper from iron (111), nickel, cobalt and magnesium by selective absorption were achieved. Copper was concentrated from very dilute solution at a flow rate of 50 ml min -1 ,and a 99% recovery was obtained. The method was applied to the rapid determination of copper in brass and bronze. A series of long-chain hydroxamic acids were synthesised and tested for suitability as stationary phase on XAD-7. Oleohydroxamic acid and naphthenohydroxamic acid were the most promising. The r ate of uptake of copper was reduced by the use of nonylphenol or amyl alcohol as a diluent. The capacities for copper of the hydroxamic acids were less when supported on XAD-7 than when used as liquid ionexchangers. The distribution coefficients of cobalt, nickel, zinc, lead, vanadium, uranium, iron (111) and copper were measured as a function of pH. XAD-7 coated with oleohydroxamic acid was used in columns for the rapid separation of iron (111) from copper and of copper from nickel, cobalt, lead and zinc. Copper was concentrated from very dilute solution at a flow rate of 45 ml min -1 and a 100,8% recovery was obtained. Copper was successfully separated from nickel by selective elution. The elution curves obtained show negligible tailing. The resin loaded with oleohydroxamic acid lost capacity due to chemical instability. Naphthenohydroxamic acid supported on XAD-7 was not suitable for use in columns, because it was physically unstable.
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  • Date Issued: 1979

Rhodes Staff Association : questions for the Vice-Chancellor

  • Authors: Henderson, Derek Scott
  • Date: 1979
  • Language: English
  • Type: text
  • Identifier: vital:7394 , http://hdl.handle.net/10962/d1017283
  • Description: Rhodes Staff Association : questions for the Vice-Chancellor, 1979
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  • Date Issued: 1979

Academic excellence, community colleges and administrative efficiency

  • Authors: Henderson, Derek Scott
  • Date: 1979
  • Language: English
  • Type: Text
  • Identifier: vital:7378 , http://hdl.handle.net/10962/d1017267
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  • Date Issued: 1979

Die vooruitsig vir Rhodes Universiteit vir 1979

  • Authors: Henderson, Derek Scott
  • Date: 1979
  • Language: Afrikaans
  • Type: text
  • Identifier: vital:7390 , http://hdl.handle.net/10962/d1017279
  • Description: Rhodes Universiteit gaan nog 'n Nuwe Jaar tegemoet, versterk en bemoedig deur die gebeure en behalings wat agter ons le. Ons het so pas, byvoorbeeld, 'n eeu van tersiere opvoeding in Grahamstad herdenk. Dit was eers in 1904 dat die baanbrekende Kollege-afdeling van St Andrew's plek gemaak het vir die nuwe Rhodes-Universiteitskollege. In September 1979 sal ons die 75ste herdenking van daardie gebeurtenis vier met 'n week van feestelikhede, insluitende 'n spesiale gradeplegtigheid, lesings, vertonings en musiek- en dramauitvoerings.
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  • Date Issued: 1979

Ntsikana's Bell

The taxonomy and osteology of fishes of the family Tripterygiidae (Perciformes : Blennioidei) of South Africa

  • Authors: Holleman, Wouter
  • Date: 1979
  • Subjects: Tripterygiidae -- South Africa , Blennioidei -- South Africa
  • Language: English
  • Type: Thesis , Masters , MSc
  • Identifier: vital:5185 , http://hdl.handle.net/10962/d1001961 , Tripterygiidae -- South Africa , Blennioidei -- South Africa
  • Description: This study is divided into two parts. The first deals with the taxonomy of the South African fishes of the Tripterygiidae. The second part describes the osteology of one genus of the family, and draws comparisons with the other genera discussed in this study. Five genera of Tripterygiidae are recognized from South African waters. Cremnochorites, a monotypic genus, is described as new. The single species, C. capensis, has been recorded only from the southern and south-eastern coast of South Africa. It is distinguished from other genera by a combination of features which includes scalation, dorsal and anal fin spine counts, and various osteological characters. Three genera, Norfolkia Fowler, Helcogramma McCulloch & Waite, and Enneapterygius Rüppell occur throughout most of the Indo-Pacific. A single species of Norfolkia, N. springeri Clark (in press) is found in Zululand. Two species are ascribed to Helcogramma, H. obtusirostre (Klunzinger) and H. fuscopinna sp.n. Parallels are drawn between two species of Tripterygion Risso, T. tripteronotus and T. delaisi from the Mediterranean. The two South African Helcogramma species show similar depth preferences to the two Tripterygion species, resulting in similar morphological differences between the two species of each pair. The genus Enneapterygius Rüppell is divided into two genera, Enneanterygius and Scoliosolen gen.n. The division is based on the form of the supraoccipital sensory canal and associated osteological characters. Sooliosolen has a crescent-shaped supraoccipital canal and cranial osteology similar to the majority of other tripterygiid genera, whereas Enneapterygius has a 'U'-shaped supraoccipital canal which curves around the first dorsal fin, a comparatively long, concave supraoccipital bone which extends anteriorly between the parietal and between the posterior ends of the frontals. Two species are referred to Scoliosolen, S. abeli (Klausewitz) and S. conspicuus (Clark), and two new species are described for Enneapterygius, E. pulcherrimus and E. trianeulus. A literature survey revealed little consistency in ascribing species to any particular genus. Thus, throughout this study an attempt is made to define the genera so that future confusion can be avoided. In the light of these definitions an assessment is made of the original descriptions of a large number of species to determine which of the species can be ascribed to Norfolkia and to Helcogramrna. This has been possible to a lesser degree for Enneapterygius and Scoliosolen, for the major external feature separating these two genera, the shape of the supraoccipital sensory canal, is described only for Red Sea (Clark, in press) and South African species (this study). This study places four species in Enneapterygius, and six in Scoliosolen. To provide a firmer foundation for defining the genera, an investigation was made of the osteology of Scoliosolen conspicuus. Enneapterygius was originally chosen for the osteolofical study as it is reputedly the largest genus of the family, and thus likely to be the most generalized. Once comparisons had been made with other Enneapterygius species, it became apparent that this genus had to be divided into two genera, Enneapterygius and Scoliosolen. It is not known whether Scoliosolen is the largest genus, but it is likely to be one of the largest once a complete survey of the species originally ascribed to Enneapterygius has been undertaken. Finally, an osteological comparison is made of the five genera which occur in South African waters to provide firmer bases for the generic definitions. Only those characters which appear to be constant within a genus are used. Reference is made to a number of genera which do not occur in South African waters, to ensure that the characters chosen cannot be applied to other genera
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  • Date Issued: 1979

Interview with Mr Hoyana

Interview with Mr Hoyana

Interview with Mr Hoyana

All Saints Hospital Golden Jubilee : All Saints, 1979

Hybridization studies within the genus Kluyveromyces van der Walt emend. van der Walt

  • Authors: Johannsen, Elz̀bieta
  • Date: 1979
  • Subjects: Yeast fungi -- Biotechnology , Yeast fungi -- Genetics , Yeast fungi -- Hybridization
  • Language: English
  • Type: Thesis , Doctoral , PhD
  • Identifier: vital:4123 , http://hdl.handle.net/10962/d1013400
  • Description: Hybridization studies based on the prototrophic selection technique, involving the use of auxotrophic mutants of strains of all accepted species of the genus Kluyveromyces, are reported. Two main groups of mutually interfertile taxa were established within the genus. The first group comprises Kluyveromyces bulgaricus, Kluyveromyces cicerisporus, Kluyveromyces dobzhanskii, Kluyveromyces drosophilarum, Kluyveromyces fragilis, Kluyveromyces lactis, Kluyveromyces marxianus, Kluyveromyces phaseolosporus, Kluyveromyces vanudenii and Kluyveromyces wikenii. The second group consists of Kluyveromyces dabzhanskii, Kluyveromyces drosophilarum, Kluyveromyces laotis, Kluyveromyces vanudenii and Kluyveromyces wiokerhamii. Hybrids were also detected in crosses involving Kluyveromyces drosophilarum and Kluyveromyces waltii as well as Kluyveromyces marxianus and Kluyveromyces thermotolerans. In terms of the concept of the biological species and in compliance with the requirements of the International Code of Botanical Nomenclature, taxa which hybridize with Kluyveromyces marxianus and form fertile recombinants at frequencies observed in intraspecific crosses, are accepted as varieties of Kluyveromyces marxianus. Hybridization was observed between Kluyveromyces marxianus var. lactis and the presumed imperfect forms of some Kluyveromyces species, namely Candida kefyr, Candida macedoniensis and Torulopsis sphaerica. Recombination was not detected in crosses involving Kluyveromyces marxianus var. marxianus and representatives of other yeast genera, i.e. Pichia, Saccharomyces, Torulaspora and Zygosaccharomyces. Conclusions regarding the relationship between members of the genus Kluyveromyces, reached on the basis of this investigation are compared with those reported by other workers, who based their investigations on phenotypic characteristics as well as on the determinations of mol % G+C and DNA-DNA homology studies.
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  • Date Issued: 1979
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