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Ingale, K. J.
- On 2-Absorbing Subtractive Ideals in Semirings
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1 Department of Mathematics, M. J. College, Jalgaon-425002, IN
1 Department of Mathematics, M. J. College, Jalgaon-425002, IN
Source
The Journal of the Indian Mathematical Society, Vol 81, No 1-2 (2014), Pagination: 23-35Abstract
In this paper, (1) a characterization of 2-absorbing ideals in the semiring (Z+0 , gcd, lcm) is obtained; (2) some characterizations of 2-absorbing subtractive ideals in a semiring R are investigated; (3) the 2-absorbing avoidance theorem for subtractive ideals of a semiring R is obtained.Keywords
Semiring, Subtractive Ideal, Prime Ideal, 2-Absorbing Ideal, Irreducible Ideal, Finitely Generated Ideal.
- On k-Regular Semirings
Abstract Views :278 |
PDF Views:10
Authors
Affiliations
1 Department of Mathematics, M. J. College, Jalgaon-425002, IN
1 Department of Mathematics, M. J. College, Jalgaon-425002, IN
Source
The Journal of the Indian Mathematical Society, Vol 82, No 3-4 (2015), Pagination: 1-11Abstract
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 Rn×n is k-regular.Keywords
Semiring, Additively Idempotent Semiring, Condition C, Q-Ideal, k-Regular Semiring, Semifield, Matrix Semiring, Quotient Semiring.- 3-Absorbing Principal T-Ideals in the Ternary Semiring of Non-positive Integers
Abstract Views :437 |
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Authors
Affiliations
1 Department of Mathematics, M. J. College, Jalgaon, IN
1 Department of Mathematics, M. J. College, Jalgaon, IN
Source
The Journal of the Indian Mathematical Society, Vol 86, No 1-2 (2019), Pagination: 38-45Abstract
Since the product of even number of elements of ternary semiring S may not be element of S, the concept of 2-absorbing ideal in S can not be defined. In this paper, we introduce the concept of 3-absorbing ideals in a commutative ternary semiring with identity element and obtain characterizations of 3-absorbing principal ideals and 3-absorbing principal T-ideals in the ternary semiring of non-positive integers.Keywords
Ternary Semiring, Prime Ideal, 3-absorbing Ideal, Finitely Generated Ideal, T-ideal.References
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