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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Sciendo
2018-06-01
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| Series: | Discussiones Mathematicae - General Algebra and Applications |
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| Online Access: | https://doi.org/10.7151/dmgaa.1284 |
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doaj-9f2cbc9187524fa6a0bf78a09cb41b702021-09-05T17:19:43ZengSciendoDiscussiones Mathematicae - General Algebra and Applications2084-03732018-06-01381476810.7151/dmgaa.1284dmgaa.1284Ideals in Ordered Γ-SemiringsRao Marapureddy Murali Krishna0Department of Mathematics GIT, GITAM University Visakhapatnam-530 045, Andhra Pradesh, IndiaIn 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.https://doi.org/10.7151/dmgaa.1284ordered γ-semiringintegral ordered γ-semiringregular or- dered γ-semiringmono ordered γ-semiringprime idealmaximal idealk- idealm− k idealfilterirreducible idealstrongly irreducible ideal16a0906f25 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Rao Marapureddy Murali Krishna |
| spellingShingle |
Rao Marapureddy Murali Krishna Ideals in Ordered Γ-Semirings Discussiones Mathematicae - General Algebra and Applications ordered γ-semiring integral ordered γ-semiring regular or- dered γ-semiring mono ordered γ-semiring prime ideal maximal ideal k- ideal m− k ideal filter irreducible ideal strongly irreducible ideal 16a09 06f25 |
| author_facet |
Rao Marapureddy Murali Krishna |
| author_sort |
Rao Marapureddy Murali Krishna |
| title |
Ideals in Ordered Γ-Semirings |
| title_short |
Ideals in Ordered Γ-Semirings |
| title_full |
Ideals in Ordered Γ-Semirings |
| title_fullStr |
Ideals in Ordered Γ-Semirings |
| title_full_unstemmed |
Ideals in Ordered Γ-Semirings |
| title_sort |
ideals in ordered γ-semirings |
| publisher |
Sciendo |
| series |
Discussiones Mathematicae - General Algebra and Applications |
| issn |
2084-0373 |
| publishDate |
2018-06-01 |
| description |
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. |
| topic |
ordered γ-semiring integral ordered γ-semiring regular or- dered γ-semiring mono ordered γ-semiring prime ideal maximal ideal k- ideal m− k ideal filter irreducible ideal strongly irreducible ideal 16a09 06f25 |
| url |
https://doi.org/10.7151/dmgaa.1284 |
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AT raomarapureddymuralikrishna idealsinorderedgsemirings |
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1717786588666134528 |