On k-Regular Semirings

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Authors

  • Department of Mathematics, M. J. College, Jalgaon-425002 ,IN
  • Department of Mathematics, M. J. College, Jalgaon-425002 ,IN

Keywords:

Semiring, Additively Idempotent Semiring, Condition C, Q-Ideal, k-Regular Semiring, Semifield, Matrix Semiring, Quotient Semiring.
Group Theory

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.

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Published

2015-12-01

How to Cite

Chaudhari, J. N., & Ingale, K. J. (2015). On k-Regular Semirings. The Journal of the Indian Mathematical Society, 82(3-4), 1–11. Retrieved from https://www.informaticsjournals.com/index.php/jims/article/view/1678

 

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