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arXiv · 1702.00810

On zero-divisors of semimodules and semialgebras

Peyman Nasehpour
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Abstract

In Section 1 of the paper, we prove McCoy's property for the zero-divisors of polynomials in semirings. We also investigate zero-divisors of semimodules and prove that under suitable conditions, the monoid semimodule $M[G]$ has very few zero-divisors if and only if the $S$-semimodule $M$ does so. The concept of Auslander semimodules are introduced in this section as well. In Section 2, we introduce Ohm-Rush and McCoy semialgebras and prove some interesting results for prime ideals of monoid semirings. In Section 3, we investigate the set of zero-divisors of McCoy semialgebras. We also introduce strong Krull primes for semirings and investigate their extension in semialgebras.

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Peyman Nasehpour. 2017-02-02. On zero-divisors of semimodules and semialgebras. https://doi.org/10.1515/gmj-2019-2071

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