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

Aman Pandey; Ajim Uddin Ansari; Tushar Singh

paper

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

arXiv:2606.27024

Abstract

In this paper, we introduce a new class of rings called Nil- $S$ -Noetherian rings, which generalizes both $S$ -Noetherian rings and $N i l_{*}$ -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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