Right $\pi$-Regular Semirings

We prove the following results (1) If $R$ is a right and left $\pi$-regular semiring then $R$ is a $\pi$-regular semiring. (2) If $R$ is an additive cancellative semiprime, right Artinian or right $\pi$-regular right Noetherian semiring then $R$ is semisimple. (3) Let $I$ be a partitioning ideal of...

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Bibliographic Details
Published inSarajevo journal of mathematics Vol. 2; no. 1; pp. 3 - 9
Main Authors Gupta, Vishnu, Chaudhari, J. N.
Format Journal Article
LanguageEnglish
Published 12.06.2024
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Summary:We prove the following results (1) If $R$ is a right and left $\pi$-regular semiring then $R$ is a $\pi$-regular semiring. (2) If $R$ is an additive cancellative semiprime, right Artinian or right $\pi$-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 $\pi$-regular then $R$ is a right $\pi$-regular semiring.   2000 Mathematics Subject Classification. 16Y60
ISSN:1840-0655
2233-1964
DOI:10.5644/SJM.02.1.01