december 2021 2-nil ideals of commutative rings
Ece Yetkin Celikel
Bull. Belg. Math. Soc. Simon Stevin 28(2): 295-304 (december 2021). DOI: 10.36045/j.bbms.201031

Abstract

The concept of 2-nil ideal of a commutative ring $R$ is introduced, as an alternative to the $(2,n)$-ideals from [6]. We study its relationship with previously introduced classes of ideals, such as 2-absorbing ideals and $n$-ideals. Various properties and examples are presented. Our main result is a characterization of rings for which every 2-nil ideal is prime. We give a description of 2-nil ideals of general ZPI-rings.

Citation

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Ece Yetkin Celikel. "2-nil ideals of commutative rings." Bull. Belg. Math. Soc. Simon Stevin 28 (2) 295 - 304, december 2021. https://doi.org/10.36045/j.bbms.201031

Information

Published: december 2021
First available in Project Euclid: 23 December 2021

Digital Object Identifier: 10.36045/j.bbms.201031

Subjects:
Primary: 13A99 , 13C13

Keywords: $n$-ideal , 2-absorbing primary ideal , 2-nil ideal , primary ideal

Rights: Copyright © 2021 The Belgian Mathematical Society

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Vol.28 • No. 2 • december 2021
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