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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…
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…
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…
-elements in multiplicative lattices -- A generalization of -ideals, -ideals and -ideals in rings
Sachin Sarode, Vinayak Joshi
In this paper, we introduce a concept of -element with respect to an -closed set in multiplicative lattices and study properties of -e…
Diameter and Girth of Zero Divisor Graph of Multiplicative Lattices
Vinayak Joshi, Sachin Sarode
In this paper, we study the zero divisor graph of a multiplicative lattice L. We prove under certain conditions that for a reduced multiplicative lattice L having more tha…
Beck's Conjecture For Multiplicative Lattices
Vinayak Joshi, Sachin Sarode
In this paper, we introduce the zero divisor graph of a multiplicative lattice. We provide a counter example to Beck's conjecture for multiplicative lattices. Further, we prove tha…