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math.AC2026
On Z-Noetherian Rings
Ambar Dubey, Tushar Singh, Shiv Datt Kumar
In this paper, introduce a new finiteness condition for commutative rings, called -Noetherian, under which every ideal contained in the set of zero-divisors is finitely g…
math.AC2026
Cohen, Levitzki, Hilbert Basis, and Lasker-Noether Theorems for Nil-S-Noetherian Rings
Aman Pandey, Ajim Uddin Ansari, Tushar Singh
In this paper, we introduce a new class of rings called Nil--Noetherian rings, which generalizes both -Noetherian rings and -Noetherian rings. We investigate several…