On Prime and semiprime ideals of $\Gamma$-semihyperrings

Document Type : Research Paper

Authors

1 Indraraj ACS college, Sillod, Dr. B. A. M. University, Aurangabad, India

2 Department of Mathematics, School of Mathematical Sciences, Kavayitri Bahinabai Chaudhari North Maharashtra University, Jalgaon, India

Abstract

The $\Gamma$-semihyperring is  a generalization of the concepts of a semiring, a semihyperring and a $\Gamma$-semiring. In this paper, the notions of completely prime ideals and prime radicals for $\Gamma$-semihyperring are introduced and studied some important properties accordingly. We also introduced the notions of $m$-system and complete $m$-system. Then characterizations of prime ideals and completely prime ideals of $\Gamma$-semihyperring with the help of $m$-system and complete $m$-system has been taken into account. It is our attempt to find a bridge between semiprime (completely semiprime) ideals and prime (completely prime) ideals of a $\Gamma$-semihyperring.

Keywords

Journal of Algebra and Related Topics
Volume 9, Issue 1
June 2021
Pages 131-141

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