On k-Regular Semirings
Keywords:
Semiring, Additively Idempotent Semiring, Condition C, Q-Ideal, k-Regular Semiring, Semifield, Matrix Semiring, Quotient Semiring.Abstract
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 Rní—n is k-regular.Downloads
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Copyright (c) 2015 J. N. Chaudhari, K. J. Ingale
This work is licensed under a Creative Commons Attribution 4.0 International License.
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