Regular Multiplicative Hyperrings

Reza Ameri, Ali Kordi

Abstract

We introduce and study regular multiplicative hyperrings, as a generalization of classical rings. Also, we use the fundamental relation ?
on a given regular multiplicative hyperring R and prove that the fundamental ring R=R/? of R is a regular ring.
Finally, we investigate the algebraic properties of M(R), the regular hyperideal of R, generated by all elements of R such that its generated hyperideals is regular.

Keywords

multiplicative hyperring, regular hyperring, fundamental relation, hyperidealregular element, idempotent

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