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){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