On $ n $-ary ring congruences of $ n $-ary semirings

Abstract

<abstract><p>In universal algebra, it is well-known that if $ S $ is an algebraic structure, then the kind of algebraic structure of $ S/\rho $ is similar to $ S $ where $ \rho $ is a congruence relation on $ S $. In this work, we study the notion of a full $ k $-ideal $ A $ of an $ n $-ary semiring $ S $ and construct a congruence relation $ \rho $ on $ S $ with respect to the full $ k $-ideal $ A $ in order to make the quotient $ n $-ary semiring $ S/\rho $ to be an $ n $-ary ring. Moreover, the notion of an $ h $-ideal of an $ n $-ary semiring was studied and connections between an $ h $-ideal and a $ k $-ideal of an $ n $-ary semiring were investigated.</p></abstract>