Siberian Federal University

For binary operations (as opposed to n-ary operations) there are useful algebraic concepts: commutativity, associativity, distributivity, etc. For n-ary operations in an associative ring, an algebraic system is proposed that represents such operations as unary operations. The composition of unary operations is binary. This system is a ring with respect to pointwise addition and multiplication. The operation of mapping composition, which is not distributive is added to the signature of the ring. Necessary and sufficient conditions are found for a congruence on this ring to be a congruence on the specified supersystem