In this article, we introduce the new concept of essential UP-filters from the concept of
essential UP-ideals in UP-algebras. Although we know that the concept of UP-ideals is UP …

The sum-essential graph 𝒮 R (M) of a left R-module M is a graph whose vertices are all
nontrivial submodules of M and two distinct submodules are adjacent if and only if their sum …

Let $ R $ be a commutative ring with unity. The essential ideal graph $\mathcal {E} _ {R} $ of
$ R $, is a graph with a vertex set consisting of all nonzero proper ideals of\textit {R} and two …

We consider superfluous elements in a bounded lattice with 0 and 1, and introduce various
types of graphs associated with these elements. The notions such as superfluous element …

Let L be a lattice. The essential element graph of L, denoted by ℰ L, is a graph whose vertex
set is the set of all nonzero proper elements of L and two vertices a and b are adjacent …

Let $ R $ be a commutative ring with unity. The essential ideal graph $\mathcal {E} _ {R} $ of
$ R $ is a graph whose vertex set consists of all nonzero proper ideals of\textit {R}. Two …

The rings considered in this article are commutative with identity and unless otherwise
specified, they are not integral domains. Let R be a ring. Let A (R) denote the set of all …

We introduce the concept of essentiality in a lattice L with respect to an element δ∈ L. We
define notions such as δ-essential, δ-uniform elements and obtain some of their properties …

Let $ R $ be a commutative ring with unity. The essential ideal graph $\mathcal {E} _R $ of $
R $ is a graph in which the vertex set comprises of set of all nonzero proper ideals of $ R …

Let S be a commutative ring with unity. The essential ideal graph of S, denoted by ES, is a
graph with vertex set consisting of all nonzero proper ideals of A and two vertices P and Q …