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Chaudhari, J. N.
- On 2-Absorbing Subtractive Ideals in Semirings
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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 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 |
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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.- On some Regularity in Semirings
Abstract Views :164 |
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Authors
Affiliations
1 Department of Mathematics, University of Delhi, Delhi-110007, IN
2 Department of Mathematics, M. J. College, Jalgaon-425002, IN
1 Department of Mathematics, University of Delhi, Delhi-110007, IN
2 Department of Mathematics, M. J. College, Jalgaon-425002, IN
Source
The Journal of the Indian Mathematical Society, Vol 76, No 1-4 (2009), Pagination: 61-68Abstract
We prove the following theorem: Let R be a right k-semiring whose every simple singular right R-semimodule is p-injective. Then (1) Every large right ideal of R is idempotent. (2) If R has no nonzero nilpotent right ideals, then R is fully right idempotent. (3) If R is right duo, then R is right π-regular.Keywords
Right Regular Semiring, Fully Right Idempotent Semiring, Right π-Regular Semiring, Singular Semimodule, p-Injective Semimodule.- 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
- Ayman Badawi, On 2-absorbing ideals of commutative rings, Bull. Austral. Math. Soc. Vol. 75(2007), 417−429.
- J. N. Chaudhari, 2-absorbing ideals in semirings, International Journal of Algebra 6(6)(2012), 265-270.
- J. N. Chaudhari, 2-absorbing ideals in the semiring of non-negative integers, Journal of the Indian Math. Soc. 80(2013), no. 3-4, 235-241.
- J. N. Chaudhari and K. J. Ingale, A note on ideals in the semiring Z+0, Journal of the Indian Math. Soc. 79(2012), no. 1-4, 33-39.
- J. N. Chaudhari and K. J. Ingale, Ideals in the ternary semiring of non-positve integers, Bull. Malaysian Math. Sci. Soc. (2) 37(4) (2014), 1149-1156.
- T. K. Dutta and S. Kar, On regular ternary semirings, Advances in Algebra, Proceedings of the ICM Satellite Conference in Algebra and Related Topics, World Scientific (2003), 343-355.
- T. K. Dutta and S. Kar, On prime ideals and prime radical of ternary semirings, Bull. Calcutta Math. Soc. 97(2005), no. 5, 445-454.
- T. K. Dutta and S. Kar, On semiprime ideals and irreducible ideals of ternary semirings, Bull. Calcutta Math. Soc. 97(2005), no. 5, 467-476.
- J. S. Golan, Semiring and their applications, Kluwer Academic publisher Dordrecht, 1999.
- V. Gupta and J. N. Chaudhari, Prime ideals in semirings, Bull. Malaysian Math. Sci. Soc., (2)34(2)(2011), 417-421.
- S. Kar, Ideal theory in the ternary semiring Z−0, Bull. Malaysian Math. Sci. Soc .(2)34(2011), no. 1, 69-77.
- W. G. Lister, Ternary rings, Trans. Amer. Math. Soc., 154(1971), 37-55.
- On Subtractive Ideals of (m; n)-semirings
Abstract Views :363 |
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Authors
Affiliations
1 M. J. College, Department of Mathematics, Jalgaon, IN
2 Dhanaji Nana Mahavidyalaya, Department of Mathematics, Faizpur, IN
1 M. J. College, Department of Mathematics, Jalgaon, IN
2 Dhanaji Nana Mahavidyalaya, Department of Mathematics, Faizpur, IN
Source
The Journal of the Indian Mathematical Society, Vol 88, No 3-4 (2021), Pagination: 275–287Abstract
Let R be a commutative (m, n)-semiring with an identity element. It is proved that every partitioning ideal of R is a subtractive ideal. Also if I is a partitioning ideal of R, then a relation between the set of subtractive ideals (subtractive prime ideals) of R containing I and the set of subtractive ideals (subtractive prime ideals) of the quotient (m, n)-semiring R/I(Q) is obtained.Keywords
(m, n)-semiring, Subtractive ideal, Partitioning ideal, Quotient (m, n)-semiringReferences
- Syed Eqbal Alam, Shrisa Rao and Bijan Davvaz, (m, n)-Semirings and a generalised fault tolerance algebra of systems, J. Appl. Math., Vol. 2013 Article ID 482391 10 pages.
- P. J. Allen, A fundamental theorem of homomorphism for semirings, Proc. Amer. Math. Soc., 21 (1969), 412-416.
- P. J. Allen, J. Neggers and H. S. Kim, Ideal theory in commutative A-semirings, Kyungpook Math. J.,46(2006), 261-271.
- Shahabaddin Ebrahimi Atani, The ideal theory in quotients of commutative semirings, Glasnik mathematicki, 42 (2007), 301-307.
- J. N. Chaudhari and K. J. Ingale, On partitioning and subtractive ideals of ternary semirings, Kyungpook Math. J., 51 (2011), 69-76.
- G. Crombez, On (n;m)-rings, Abh. Math. Sem. Univ. Hamburg, 37 (1972), 180-199.
- A. Pop, Remarks on Embedding Theorems of (m; n)-Semirings, Bul. Stiint. Univ. Baia Mare Ser. B, Mathematica-Informatica 16(2000), 297-302.
- Adina Pop and M. Lauran, A Note on the Morphism theorems for (n;m)-Semirings, Creat. Math. Inform., 27 (1) (2018), 79-88.
- Maria S. Pop and Adina Pop, Some properties of generalized semirings, Carpathian J. Math 24 No. 3(2008), 397-402.
- Y. Zhu, On the Jacobson radical of (m,n)-semirings, Algebra 2013, Article ID 272104, 9 pages.