Right $π$-Regular Semirings - Gupta, Vishnu; Chaudhari, J. N. (Sarajevo Journal of Mathematics, 2024)
We prove the following results (1) If $R$ is a right and left $π$-regular semiring then $R$ is a $π$-regular semiring. (2) If $R$ is an additive cancellative semiprime, right Artinian or right $π$-regular right Noetherian semiring then $R$ is semisimple. (3) Let $I$ be a partitioning ideal of a semiring $R$ such that $Q=(R-I)\cup \{0\}$. If $I$ is a right regular ideal and the quotient semiring $R/I$ is right $π$-regular then $R$ is a right $π$-regular semiring. 2000 Mathematics Subject Classification. 16Y60