# Fundamental relation onm-idempotent hyperrings

Morteza Norouzi; Irina Cristea

Open Mathematics (2017)

- Volume: 15, Issue: 1, page 1558-1567
- ISSN: 2391-5455

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topMorteza Norouzi, and Irina Cristea. "Fundamental relation onm-idempotent hyperrings." Open Mathematics 15.1 (2017): 1558-1567. <http://eudml.org/doc/288430>.

@article{MortezaNorouzi2017,

abstract = {The γ*-relation defined on a general hyperring R is the smallest strongly regular relation such that the quotient R/γ* is a ring. In this note we consider a particular class of hyperrings, where we define a new equivalence, called [...] εm∗ $\varepsilon ^\{*\}_\{m\} $, smaller than γ* and we prove it is the smallest strongly regular relation on such hyperrings such that the quotient R/ [...] εm∗ $\varepsilon ^\{*\}_\{m\} $ is a ring. Moreover, we introduce the concept of m-idempotent hyperrings, show that they are a characterization for Krasner hyperfields, and that [...] εm∗ $\varepsilon ^\{*\}_\{m\} $ is a new exhibition for γ* on the above mentioned subclass of m-idempotent hyperrings.},

author = {Morteza Norouzi, Irina Cristea},

journal = {Open Mathematics},

keywords = {Hyperring; m-idempotent; Strongly regular relation},

language = {eng},

number = {1},

pages = {1558-1567},

title = {Fundamental relation onm-idempotent hyperrings},

url = {http://eudml.org/doc/288430},

volume = {15},

year = {2017},

}

TY - JOUR

AU - Morteza Norouzi

AU - Irina Cristea

TI - Fundamental relation onm-idempotent hyperrings

JO - Open Mathematics

PY - 2017

VL - 15

IS - 1

SP - 1558

EP - 1567

AB - The γ*-relation defined on a general hyperring R is the smallest strongly regular relation such that the quotient R/γ* is a ring. In this note we consider a particular class of hyperrings, where we define a new equivalence, called [...] εm∗ $\varepsilon ^{*}_{m} $, smaller than γ* and we prove it is the smallest strongly regular relation on such hyperrings such that the quotient R/ [...] εm∗ $\varepsilon ^{*}_{m} $ is a ring. Moreover, we introduce the concept of m-idempotent hyperrings, show that they are a characterization for Krasner hyperfields, and that [...] εm∗ $\varepsilon ^{*}_{m} $ is a new exhibition for γ* on the above mentioned subclass of m-idempotent hyperrings.

LA - eng

KW - Hyperring; m-idempotent; Strongly regular relation

UR - http://eudml.org/doc/288430

ER -

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