Distinguished elements in semiring extensions
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2018
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| _version_ | 1866917570715582464 |
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| author | Nasehpour, Peyman |
| author_facet | Nasehpour, Peyman |
| contents | In this paper, we investigate zero-divisor, nilpotent, idempotent, unit, small, and irreducible elements in semiring extensions such as amount, content, and monoid semialgebras. We also introduce new concepts such as the prime avoidance property in semirings, entire-like semirings, semialgebras with Property (A), and also, Armendariz and McCoy semialgebras and we prove some results related to these concepts. For example, we prove that if $B$ is an $S$-semialgebra, then under some conditions, the set of zero-divisors $Z(B)$ of $B$ is the union of the extended maximal primes of $Z(S)$. Finally, we prove a generalization of Eisenstein's irreducibility criterion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1811_02142 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Distinguished elements in semiring extensions Nasehpour, Peyman Commutative Algebra 16Y60, 12K10, 13A15 In this paper, we investigate zero-divisor, nilpotent, idempotent, unit, small, and irreducible elements in semiring extensions such as amount, content, and monoid semialgebras. We also introduce new concepts such as the prime avoidance property in semirings, entire-like semirings, semialgebras with Property (A), and also, Armendariz and McCoy semialgebras and we prove some results related to these concepts. For example, we prove that if $B$ is an $S$-semialgebra, then under some conditions, the set of zero-divisors $Z(B)$ of $B$ is the union of the extended maximal primes of $Z(S)$. Finally, we prove a generalization of Eisenstein's irreducibility criterion. |
| title | Distinguished elements in semiring extensions |
| topic | Commutative Algebra 16Y60, 12K10, 13A15 |
| url | https://arxiv.org/abs/1811.02142 |