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arXiv · 2606.27024

Cohen, Levitzki, Hilbert Basis, and Lasker-Noether Theorems for Nil-S-Noetherian Rings

Aman Pandey·Ajim Uddin Ansari·Tushar Singh
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Abstract

In this paper, we introduce a new class of rings called Nil-$S$-Noetherian rings, which generalizes both $S$-Noetherian rings and $Nil_{*}$-Noetherian rings. We investigate several properties of this new class and establish generalized versions of some classical results, including Cohen's theorem, Levitzki's theorem, and Hilbert's basis theorem. Furthermore, we prove $S$-version of classical Lasker-Noether theorem for Nil-$S$-Noetherian rings.

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Aman Pandey, Ajim Uddin Ansari, Tushar Singh. 2026-06-25. Cohen, Levitzki, Hilbert Basis, and Lasker-Noether Theorems for Nil-S-Noetherian Rings. https://arxiv.org/abs/2606.27024

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