- Title
- On the ideals and semimodules of commutative semirings
- Creator
- Olivier, Ruan
- Subject
- Gqeberha (South Africa)
- Subject
- Eastern Cape (South Africa)
- Subject
- South Africa
- Date Issued
- 2021-04
- Date
- 2021-04
- Type
- Master's theses
- Type
- text
- Identifier
- http://hdl.handle.net/10948/52782
- Identifier
- vital:44026
- Description
- Semirings are a generalisation of rings where additive inverses need not exist. In this dissertation, we focus on results of commutative semirings with non-zero identity. Many results that we study are analogous to results from commutative rings with non-zero identity. Properties which are unique to semirings are also investigated, such as semirings where all elements are additively idempotent. The notion of ideals is examined in the context of a semiring. Specifically, prime ideals, maximal ideals, k-ideals and partitioning ideals of semirings are considered. Additionally, the module over a ring is generalised to a semimodule over a semiring. The emphasis is on prime subsemimodules and multiplication semimodules. Lastly, invertible ideals of semirings are examined.
- Description
- Thesis (MSc) -- Faculty of Science, School of Computer Science, Mathematics, Physics and Statistics, 2021
- Format
- computer
- Format
- online resource
- Format
- application/pdf
- Format
- 1 online resource (93 pages)
- Format
- Publisher
- Nelson Mandela University
- Publisher
- Faculty of Science
- Language
- English
- Rights
- Nelson Mandela University
- Rights
- All Rights Reserved
- Rights
- Open Access
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| Thumbnail | File | Description | Size | Format | |||
|---|---|---|---|---|---|---|---|
| View Details Download | SOURCE1 | Olivier, R.pdf | 737 KB | Adobe Acrobat PDF | View Details Download |