On K-regular Additive Ternary Semirings

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Authors

  • Kunal Julal Ingale
     Department of Mathematics, M. J. College, Jalgaon - 425002 ,IN
  • Hemant Premraj Bendale
     Department of Mathematics, M. J. College, Jalgaon - 425002 ,IN
  • Dipak Ravindra Bonde
     Department of Mathematics, ACS College, Dharangaon - 425 105 ,IN
  • Jayprakash Ninu Chaudhari
     Department of Mathematics, M. J. College, Jalgaon - 425002 ,IN

DOI:

https://doi.org/10.18311/jims/2022/29309

Keywords:

Additive ternary semiring, additively idempotent additive ternary semiring, k-regular additive ternary semiring, k-invertible additive ternary semiring

Abstract

We introduce the concepts of a k-regular and a k-invertible additive ternary semiring. We show that (i) If I is a k-regular ideal of an additive ternary semiring S and J is any ideal of S, then I ? J is a k-regular ideal of S; (ii) If S is an additively idempotent, commutative additive ternary semiring and x ? S, then M (x) is a commutative additive ternary monoid of (S, +); (iii) An additively idempotent additive ternary semiring S is k-regular if and only if S is k-invertible; (iv) Let S be an additively and lateral cancellative additive ternary semiring. If a, b ? S, then V (a) and V (b) are either disjoint or equal.

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Published

2022-01-27

How to Cite

Julal Ingale, K., Premraj Bendale, H., Ravindra Bonde, D., & Ninu Chaudhari, J. (2022). On <i>K</i>-regular Additive Ternary Semirings. The Journal of the Indian Mathematical Society, 89(1-2), 72–83. https://doi.org/10.18311/jims/2022/29309

Issue

Volume 89, Issue 1-2, January-June 2022

Section

Articles

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Copyright (c) 2022 Kunal Julal Ingale, Hemant Premraj Bendale, Dipak Ravindra Bonde, Jayprakash Ninu Chaudhari

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

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Europe PMC
Received 2022-01-11
Accepted 2023-01-30
Published 2022-01-27

 

References

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