A note on isomorphism theorems of Krasner (m, n)-hyperrings

S Ostadhadi-Dehkordi,B Davvaz

doi:10.1007/s40065-015-0143-8

S Ostadhadi-Dehkordi, B Davvaz

Open Access

https://doi.org/10.1007/s40065-015-0143-8

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Abstract

Recently, Krasner (m, n)-hyperrings were introduced and analyzed by Davvaz et. al. This is a suitable generalization of Krasner hyperrings. In this research work, we consider that if I is a normal hyperideal of a Krasner (m, n)-hyperring R, then the quotient hyperring [R : I*] is an (m, n)-ring. Moreover, we prove that if R is a multiplicative (m, n)-ary hyperring and I is a normal hyperideal of R, then [R : I*] is an (m, n)-ring.

Highlights

Hypergroups were introduced in 1934 by a French mathematician Marty [14] at the Congress of Scandinavian Mathematicians
Hyperstructures have a lot of applications in several domains of mathematics and computer science [1,5,13, 18, 20, 21]
In [7], Davvaz and Vougiouklis introduced the concept of n-ary hypergroups as a generalization of hypergroups in the sense of Marty which is a suitable generalization of n-ary groups

Summary

Introduction

Hypergroups were introduced in 1934 by a French mathematician Marty [14] at the Congress of Scandinavian Mathematicians. We prove that if R is a multiplicative (m, n)-ary hyperring and I is a normal hyperideal of R, [R : I ∗] is an (m, n)-ring. Let (R, f, g) be a Krasner (m, n)-hyperring and ρ be an equivalence relation on R. Definition 2.7 The equivalence relation ρ on an m-ary hypergroup (R, f ) is called regular if for all x2, x3, .

Results

Conclusion