Right $\pi$-Regular Semirings
DOI:
https://doi.org/10.5644/SJM.02.1.01Keywords:
Semiring, subtractive ideal, partitioning ideal, quotient semiring, right $\pi$-regular semiring, right regular semiring, $\pi$-regular semiring, regular semiring, right semiregular right ideal, Jacobson-Bourne radical, semiprime semiring, semisimple semiring, right Arthinian semiring, right Noetherian semiringAbstract
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
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References
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