On k-Regular Semirings
2015
Generalizing the notion of regular ring in the sense of Von Neumann, Bourne, Adhikari, Sen and Wienert introduced the notion of k-regular semiring. In this paper, we investigate Q-ideals of the semiring of non-negative integers for which the quotient semiring is a semifield and a k-regular semiring. Also we prove that a semiring R is k-regular if and only if the quotient semiring R/I is k-regular for every Q-ideal I of R. Finally we prove that if R is an additively idempotent semiring with identity, then R is k-regular if and only if the matrix semiring R n×n is k-regular.
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