A ring or an idempotent semiring is associative provided that additive endomorphisms are multiplicative.

Semiring is an algebraic structure of (S, +, ×). Similar to a ring, but without the condition that each element must have inverse adding operation. The forms +) and ×) are semigroups satisfy distributive law multiplication addition. In matrix theory, there term known as Kronecker product. This operation transforms two matrices into larger containing all possible products entries in matrices. pr...

We determine the automorphism group of zero-divisor digraph semiring matrices over an antinegative commutative with a finite number zero-divisors.

We suggest a version of Nullstellensatz over the tropical semiring, the real numbers equipped with operations of maximum and summation.