3 papers
math.AC2026
On -prime and -primary elements in multiplicative lattices
Sachin Sarode, Chetan Patil, Vinayak Joshi
In this paper, we study -prime elements and -primary elements within the framework of multiplicative lattices. Furthermore, we define and explore weakly -prime elements an…
math.AC2026
On -Noetherian Lattices
Sachin Sarode, Chetan Patil, Vinayak Joshi
In this paper, we define and study -Noetherian lattices as a natural generalization of Noetherian rings. We prove that a ring is -Noetherian if and only if its ideal latt…
math.AC2026
On -Prime Element Principle
Sachin Sarode, Chetan Patil, Vinayak Joshi
In this paper, we introduce -prime elements in -lattices, where is a multiplicatively closed subset of a -lattice . In addition, we introduce the -Prime Element…