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On Regular Multiplicative Hyperrings

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Abstract (2. Language): 
We introduce and study regular multiplicative hyperrings, as a generalization of classical rings. Also, we use the fundamental relation R 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 hyperideal is regular.
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