1 citations · 1 across the 13 of their papers we have counts for
14 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-complement…
Cohen-Macauleyness of the Zero-Divisor Graph of a Boolean Poset
P. Waghmare, V. Joshi
In this paper, we prove that the zero-divisor graph of a Boolean poset is both well-covered and Cohen--Macaulay. Furthermore, for a poset $\mathbf{P} = \prod_{i=1}^{n} P…
Component graphs of vector spaces and zero-divisor graphs of ordered sets
Nilesh Khandekar, Peter J. Cameron, Vinayak Joshi
In this paper, nonzero component graphs and nonzero component union graphs of finite dimensional vector space are studied using the zero-divisor graph of specially constructed 0-1-…
Coloring of zero-divisor graphs of posets and applications to graphs associated with algebraic structures
Nilesh Khandekar, Vinayak Joshi
In this paper, we characterize chordal and perfect zero-divisor graphs of finite posets. Also, it is proved that the zero-divisor graphs of finite posets and the complement of zero…
-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…
Zero-divisor graphs of lower dismantlable lattices-II
Avinash Patil, B. N. Waphare, Vinayak Joshi
In this paper, we continue our study of the zero-divisor graphs of lower dismantlable lattices that was started in [20]. The present paper mainly deals with an Isomorphism Problem…
Zero-divisor graphs of lower dismantlable lattices-I
Avinash Patil, B. N. Waphare, Vinayak Joshi +1
In this paper, we study the zero-divisor graphs of a subclass of dismantlable lattices. These graphs are characterized in terms of the non-ancestor graphs of rooted trees.
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…