6 papers
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…
On S-Integral Domains and S-Version of Krull Intersection Theorem
Tushar Singh, Gyanendra K. Verma, Shiv Datt Kumar
Let be a multiplicatively closed subset of a ring . We extend several results on integral domains to their -versions and establish the -version of Krull int…
Structural Analysis of Commutative S-Reduced Rings
Tushar Singh, Shiv Datt Kumar
Let be a commutative ring with identity, be a multiplicative set. In this paper, we establish that the intersection of all -prime ideals in an -reduced ri…
On S-J-Noetherian Rings
Tushar Singh, Ajim Uddin Ansari, Shiv Datt Kumar
Let be a commutative ring with identity, be a multiplicative set and be an ideal of . In this paper, we introduce the concept of --Noetherian rings,…
Nonnil-S-Laskerian Rings
Tushar Singh, Ajim Uddin Ansari, Shiv Datt Kumar
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 i…
A Study of S-Primary Decompositions
Tushar Singh, Ajim Uddin Ansari, Shiv Datt Kumar
Let be a commutative ring with identity and be a multiplicative set. An ideal of (disjoint from ) is said to be -primary if there exists an $s\in…