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http://dx.doi.org/10.5666/KMJ.2019.59.1.35

On Regular Γ-semihyperrings and Idempotent 𝚪-semihyperrings  

Pawar, Kishor Fakira (Department of Mathematics, School of Mathematical Sciences, Kavayitri Bahinabai Chaudhari North Maharashtra University)
Patil, Jitendra Jaysing (Department of Mathematics, Indraraj Arts, Commerce & Science College)
Davvaz, Bijan (Department of Mathematics, Yazd University)
Publication Information
Kyungpook Mathematical Journal / v.59, no.1, 2019 , pp. 35-45 More about this Journal
Abstract
The ${\Gamma}$-semihyperring is a generalization of the concepts of a semiring, a semihyperring and a ${\Gamma}$-semiring. Here, the notions of (strongly) regular ${\Gamma}$-semihyperring, idempotent ${\Gamma}$-semihyperring; invertible set, invertible element in a ${\Gamma}$-semihyperring are introduced, and several examples given. It is proved that if all subsets of ${\Gamma}$-semihyperring are strongly regular then for every ${\Delta}{\subseteq}{\Gamma}$, there is a ${\Delta}$-idempotent subset of R. Regularity conditions of ${\Gamma}$-semihyperrings in terms of ideals of ${\Gamma}$-semihyperrings are also characterized.
Keywords
${\Gamma}$-semihyperring; regular (strongly regular) ${\Gamma}$-semihyperring; idempotent ${\Gamma}$-semihyperring;
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