Refine your search
Collections
Co-Authors
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z All
Chaudhari, Jayprakash Ninu
- 2-Absorbing Ideals in the Semiring of Non-Negative Integers
Abstract Views :381 |
PDF Views:1
Authors
Affiliations
1 Department of Mathematics, M. J. College, Jalgaon-425 002, IN
1 Department of Mathematics, M. J. College, Jalgaon-425 002, IN
Source
The Journal of the Indian Mathematical Society, Vol 80, No 3-4 (2013), Pagination: 235-241Abstract
All 2-absorbing ideals in the semiring of non-negative integers are investigated.Keywords
Semiring, Prime Ideal, 2-Absorbing Ideal, Finitely Generated Ideal.
- A Remark on n-absorbing Ideals of Principal Ideal Domains
Abstract Views :212 |
PDF Views:0
Authors
Affiliations
1 Department of Mathematics M. J. College, Jalgaon - 425 002, IN
1 Department of Mathematics M. J. College, Jalgaon - 425 002, IN
Source
The Journal of the Indian Mathematical Society, Vol 81, No 3-4 (2014), Pagination: 227-229Abstract
Let R be a commutative ring with identity 1 ≠ 0. General-izing the notion of prime ideals in R, Anderson and Badawi introduced the notion of n-absorbing ideals in R. We introduce the notion of n- absorbing domains which is a generalization of an integral domain. We investigate all n-absorbing ideals in a PID R and hence prove that Zm is an n-absorbing domain if and only if m = p1r1 p2r2 p3r3 …pkrk where k ≤ n and r1 + r2 + r3 + … + rk ≤ n.Keywords
Principal Ideal Domain, n-Absorbing Ideal, n-Absorbing Domain.References
- D. F. Anderson and Ayman Badawi, On n-absorbing ideals of commutative rings, Comm. Algebra 39(2011), 1646 – 1672.
- Ayman Badawi, On 2-absorbing ideals of commutative rings, Bull. Austral. Math. Soc. Vol. 75(2007), 417 – 429.
- I. N. Herstein, Topics in algebra, Blaisdell Publishing company, 1964.
- Sh. Payrovi and S. Babaei, On the 2-absorbing ideals in commutative rings, Bull.Malays. Math. Sci. Soc. (To appear).
- On B-Ideals in Semirings
Abstract Views :286 |
PDF Views:4
Authors
Affiliations
1 Department of Mathematics, ACS College, Dharangaon 425 105,, IN
2 Department of Mathematics, M. J. College, Jalgaon 425002, IN
1 Department of Mathematics, ACS College, Dharangaon 425 105,, IN
2 Department of Mathematics, M. J. College, Jalgaon 425002, IN
Source
The Journal of the Indian Mathematical Society, Vol 87, No 1-2 (2020), Pagination: 1-8Abstract
In this paper, we introduce the notion of B-ideal in a commutative semiring R. Then 1) A characterization of B-ideals in the Semiring of non-negative integers is obtained. 2) Relation between B-ideals in a semiring R containing a Q-ideal I of R and B-ideals in the quotient semiring R/I(Q) is obtained. Further study of k-Noetherian semirings is developed. Also B-ideals in polynomial semirings are studied.Keywords
Semiring, Zerosumfree Semiring, Subtractive Ideal, Partitioning Ideal, B-ideal, Strong B-ideal, Quotient Semiring, K-Noetherian Semiring, Polynomial Semiring, Monic Ideal, Coefficient Ideal.References
- Paul J. Allen, A fundamental theorem of homomorphism for semirings, Proc. Amer. Math. Soc., 21. (1969), 412-416.
- Shahabaddin Ebrahimi Atani, The ideal theory in quotients of commutative semirings, Glasnik Matematicki, 42. (62)(2007), 301-308.
- J. N. Chaudhari and D. R. Bonde, Ideal theory in quotient semirings, Thai J. Math., 12. (1) (2014), 95-101.
- J. N. Chaudhari, 2-absorbing ideals in semirings, Inter. J. Alg., 6(6)(2012), 265-270.
- J. N. Chaudhari and V. Gupta, Weak primary decomposition theorem for right Noetherian semirings, Indian J. Pure and Appl. Math, 25. (6)(1994), 647-654.
- L. Dale, Monic and monic free ideals in polynomial semiring, Proc. Am. Math. Soc., 56(1) (1976), 45-50.
- A. Y. Darani, On 2-Absorbing and Weakly 2-Absorbing Ideals of Commutative Semirings, Kyungpook Math. J., 52(2012), 91-97.
- J. S. Golan, Semirings and Their Applications, Kluwer, Dordrecht, 1999.
- Vishnu Gupta and J. N. Chaudhari, On partitioning ideals of semirings, Kyungpook Math. J., 46. (2006), 181-184.
- V. Gupta and J. N. Chaudhari, On prime ideals in semirings, Bull. Malaysian Math. Sc. Soc., 34(2) (2011), 417–421.
- T. K. Mukherjee, M. K. Sen and Shamik Ghosh, Chain Conditions on Semirings, Internat. J. Math. and Math. Sci., 19(2)(1996), 321-326.