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

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.