Ideals in Ordered Γ-Semirings
In this paper, we introduce the notion of k-ideal, m−k ideal, prime ideal, maximal ideal, filter, irreducible ideal, strongly irreducible ideal in ordered Γ-semirings, study the properties of ideals in ordered Γ-semirings and the relations between them. We characterize m − k ideals using derivation...
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| Format: | Article |
| Language: | English |
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Sciendo
2018-06-01
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| Series: | Discussiones Mathematicae - General Algebra and Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.7151/dmgaa.1284 |
| Summary: | In this paper, we introduce the notion of k-ideal, m−k ideal, prime ideal, maximal ideal, filter, irreducible ideal, strongly irreducible ideal in ordered Γ-semirings, study the properties of ideals in ordered Γ-semirings and the relations between them. We characterize m − k ideals using derivation of ordered Γ-semirings and prove that every ideal in a mono regular ordered Γ-semiring is a prime ideal and field ordered Γ-semiring is simple. |
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| ISSN: | 2084-0373 |