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Julal Ingale, Kunal
- On K-regular Additive Ternary Semirings
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Authors
Affiliations
1 Department of Mathematics, M. J. College, Jalgaon - 425002, IN
2 Department of Mathematics, ACS College, Dharangaon - 425 105, IN
1 Department of Mathematics, M. J. College, Jalgaon - 425002, IN
2 Department of Mathematics, ACS College, Dharangaon - 425 105, IN
Source
The Journal of the Indian Mathematical Society, Vol 89, No 1-2 (2022), Pagination: 72–83Abstract
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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