Fundamental relation onm-idempotent hyperrings

Morteza 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 -