7 papers
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 Isomorphism theorem of the Comparability Graph of Lattices
Rahul Jejurkar, Vinayak Joshi
In recent years, researchers have actively contributed to the field of graphs associated with algebraic structures and ordered structures. It is a fundamental question to ask wheth…
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…
A Proof of the Conjecture on complemented zero-divisor graphs of semigroups
Anagha Khiste, Ganesh Tarte, Vinayak Joshi
In this paper, we are motivated by the conjectures proposed by C.~Bender \textit{et al.}, \cite{C} in 2024. We have settled the first two conjectures negatively by providing a coun…
Complemented zero-divisor graph of posets
Anagha Khiste, Ganesh Tarte, Vinayak Joshi
In this paper, we derive a set of equivalent conditions for the zero-divisor graph of a poset with to be complemented, characterizing it in terms of quasi-complemen…