The Journal of the Indian Mathematical Society

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On K-regular Additive Ternary Semirings


Affiliations
1 Department of Mathematics, M. J. College, Jalgaon - 425002, India
2 Department of Mathematics, ACS College, Dharangaon - 425 105, India
     

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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.


Keywords

Additive Ternary Semiring; Additively Idempotent Additive Ternary Semiring; K-Regular Additive Ternary Semiring; K-Invertible Additive Ternary Semiring.
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  • On K-regular Additive Ternary Semirings

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Authors

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

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.


Keywords


Additive Ternary Semiring; Additively Idempotent Additive Ternary Semiring; K-Regular Additive Ternary Semiring; K-Invertible Additive Ternary Semiring.

References





DOI: https://doi.org/10.18311/jims%2F2022%2F29309