Almost δ-primary ideals in a commutative ring

Document Type : Research Paper

Authors

1 Department of Engineering Science And Humanities, JSPM's Rajarshi Shahu College of Engineering Tathawade, Pune, India

2 Department of Engineering science, Shreeyash college of engineering and technology, Chhatrapati Sambhajinagar

Abstract

In this paper, our research sheds new light on generalized ideals, significantly advancing the state of knowledge in ring theory. We introduce an almost δ-primary ideal which unifies an almost prime ideal and an almost primary ideal. We also define and study the concept of a φ-δ-primary ideal in a commutative ring. Some characterizations of almost δ-primary ideal and n-almost δ-primary ideals are proved. 

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References

[1] D. D. Anderson and M. Bataineh, Generalizations of prime ideals, Comm. Algebra, 36(2)(2008), 686-696.
[2] D. D. Anderson and E. Smith, Weakly prime ideals, Houston J. Math., 29 (2003), 831-840.
[3] A. Badawi and B. Fahid, On weakly 2-absorbing δ-primary idelas of commutative rings, Georgian Math. J., 27(4) (2018), 1–13.
[4] M. Bataineh and S. Kuhail, Generalizations of primary ideals and submodules, Int. J. of Contemporary Math. Sci., 6 (2011), 811–824.
[5] A. Darani and Yousefian , Generalizations of primary ideals in commutative rings, Novi Sad J. Math., 42(1) (2012),27-35.
[6] B. Fahid and D. Zhao , 2-absorbing δ-primary idelas of commutative rings, Kyungpook Math. J., 57 (2017), 193-198.
[7] C. S. Manjrekar and A.V. Bingi, ϕ-prime and ϕ-primary elements in multiplicative lattices, Hindawi Publishing  Corporation Alg., (2014).
[8] S. K. Nimbhorkar and J. Y. Nehete, Generalizations of δ-primary elements in multiplicative lattices.,Palest. J. Math. 10(1) (2021), 78–85.
[9] D. Zhao, δ-primary ideals of commutative rings, Kyungpook Math. J., 41 (2001), 17-22. 
Journal of Hyperstructures
Volume 14, Issue 1
2025
Pages 36-46

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