Congruences on left almost rings

Abstract

The aim of this paper is to characterize left almost rings by congruence relations. We show that each homomorphism of left almost rings defines a congruence relation on left almost rings. We then discuss quotient left almost rings. At the end we prove analogue of the isomorphism theorems for left almost rings.

Literature Survey on Non-Associative Rings and Developments

“…Recently, in 2015, Hussain and W. Khan [104] characterized LA-rings by congruence relations. They had shown that each homomorphism of LA-rings defines a congruence relation on LA-rings.…”

“…Some characterizations of left primary and weakly left primary ideals are obtained. Moreover, in 2015 Hussain and Khan [104] have characterized LA-rings by congruence relations. They proved that each homomorphism of left almost rings defines a congruence relation on left almost rings.…”