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arXiv · 2512.14519

Nonnil-S-Laskerian Rings

Tushar Singh·Ajim Uddin Ansari·Shiv Datt Kumar
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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.

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Tushar Singh, Ajim Uddin Ansari, Shiv Datt Kumar. 2025-12-16. Nonnil-S-Laskerian Rings. https://arxiv.org/abs/2512.14519

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