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On zero-divisors of semimodules and semialgebras

  • Peyman Nasehpour ORCID logo EMAIL logo

Abstract

We prove McCoy’s property for the zero-divisors of polynomials in semirings, investigate the 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 is introduced as well. Then we introduce Ohm–Rush and McCoy semialgebras and prove some interesting results for prime ideals of monoid semirings. Finally, we investigate the set of zero-divisors of McCoy semialgebras. We also introduce strong Krull primes for semirings and investigate their extension in semialgebras.


Dedicated to my mother


Funding statement: This work is supported by Golpayegan University of Technology. Our special thanks go to the Department of Engineering Science in Golpayegan University of Technology for providing all the necessary facilities available to us for successfully conducting this research.

Acknowledgements

We like to thank Prof. Dara Moazzami, the ex-President of Golpayegan University of Technology, for his help, motivation, and encouragement. We are also grateful to the anonymous referee.

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Received: 2018-05-29
Revised: 2018-07-14
Accepted: 2018-07-19
Published Online: 2019-11-27
Published in Print: 2021-06-01

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