Nonnil-S-Laskerian Rings
Commutative Algebra
2025-12-17 v1
Abstract
In this paper, we introduce the concept of nonnil-S-Laskerian rings, which generalize both nonnil-Laskerian rings and S-Laskerian rings. A ring R is said to be nonnil-S-Laskerian if every nonnil ideal I (disjoint from S) of R is S-decomposable. As a main result, we prove that the class of nonnil-S-Noetherian rings belongs to the class of nonnil-S-Laskerian rings. Also, we prove that a nonnil-S-Laskerian ring has S-Noetherian spectrum under a mild condition. Among other results, we prove that if the power series ring R[[X]] is nonnil-S-Laskerian with S-decomposable nilradical, then R is S-laskerian and satisfies the S-SFT property.
Keywords
Cite
@article{arxiv.2512.14519,
title = {Nonnil-S-Laskerian Rings},
author = {Tushar Singh and Ajim Uddin Ansari and Shiv Datt Kumar},
journal= {arXiv preprint arXiv:2512.14519},
year = {2025}
}