Journal of Mathematics and Applications
07/38, DOI: 10.7862/rf.2015.7
Some results on 2-absorbing ideals in commutative semirings
Pratibha Kumar, Manish Kant Dubey, Poonam Sarohe
DOI: 10.7862/rf.2015.7
Abstract
In this paper, we study the concepts of 2-absorbing and weakly 2-absorbing ideals in a commutative semiring with non-zero identity which is a generalization of prime ideals of a commutative semiring and prove number of results related to the same. We also use these concepts to prove some results of Q-ideals in terms of subtractive extension of ideals in a commutative semiring.
References
- Allen P. J.: A fundamental theorem of homomorphism for semirings, Proc. Amer. Math. Soc., 21(1969), 412-416.
- Anderson, D. D., Bataineh, M.: Generalizations of prime ideals, Comm. Algebra, 36(2),(2008), 686-696.
- Anderson, D. D. and Smith, Eric: Weakly prime ideals, Houston J. Math., 29 (2003), 831-840.
- Atani, R. E. and Atani, S. E.: Spectra of semimodules; Bul. Acad. De Stiinte, A Republicii Moldova. Math., 3(67), (2011), 15-28.
- Badawi, A.: On
2-absorbing ideals of commutative rings, Bull Austral. Math. Soc., 75(2007), 417-429. - Badawi, A. and Darani, A. Y.: On weakly 2-absorbing ideals of commutative rings, Houston J. Math., 39(2), (2013), 441-452.
- Chaudhari, J. N. and Bonde, D. R.: Ideal theory in quotient semirings, Thai J. Of Math., Vol.12, (2014), 95-101.
- Darani, A. Y.: On 2-absorbing and weakly 2-absorbing ideals of commutative Semirings, Kyungpook Math. J., 52(1), (2012), 91-97.
- Dubey, M. K.: Prime and weakly prime ideals in semirings, Quasigroups and Related Systems, 20 (2012), 151-156.
- Dubey, M. K. and Sarohe, P.: On 2-absorbing semimodules, Quasigroups and Related Systems, 21 (2013), 175-184.
- Golan, J. S. : Semirings and their applications, Kluwer Academic Publishers, Dordrecht, (1999).
- Gupta,V. and Chaudhari, J. N.: Characterization of weakly prime subtractive ideals in semirings, Bull. Inst. Math. Acad. Sin. (N.S.), 3(2) (2008), 347-352.
- Payrovi, Sh. and Babaei, S.: On the 2-absorbing ideals in commutative rings, Bull. Malaysian Math. Sci., 23, (2013), 1511-1526.
- Vandiver H. S.: Note on a Simple type of Algebra in Which the Cancellation Law of Addition Does Not Hold, Bull. Amer. Math. Soc., 40(3), (1934) 916-920.
About this Article
TITLE:
Some results on 2-absorbing ideals in commutative semirings
AUTHORS:
Pratibha Kumar (1)
Manish Kant Dubey (2)
Poonam Sarohe (3)
AUTHORS AFFILIATIONS:
(1) Department of Mathematics, Kirori Mal College, University of Delhi, Delhi 110007, India
(2) Department of Mathematics, Lakshmibai College, University of Delhi, Delhi 110052, India
(3) Department of Mathematics, Lakshmibai College, University of Delhi, Delhi 110052, India
JOURNAL:
Journal of Mathematics and Applications
07/38
KEY WORDS AND PHRASES:
Semiring, subtractive ideal, 2-absorbing ideal, weakly 2-absorbing ideal, subtractive extension of an ideal, Q-ideal
FULL TEXT:
http://doi.prz.edu.pl/pl/pdf/jma/34
DOI:
10.7862/rf.2015.7
URL:
http://dx.doi.org/10.7862/rf.2015.7
RECEIVED:
2014-05-16
COPYRIGHT:
Publishing House of Rzeszow University of Technology Powstańców Warszawy 12, 35-959 Rzeszow