On n-ary ring congruences of n-ary semirings

Abstract

In universal algebra, it is well-known that if S is an algebraic structure, then the kind of algebraic structure of S/ρ is similar to S where ρ 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 ρ on S with respect to the full k-ideal A in order to make the quotient n-ary semiring S/ρ 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.

Keywords

• n-ary ring
• n-ary semiring
• ring congruence
• k-ideal
• h-ideal