Results 51 to 60 of about 180 (93)
A Submodule-Based Zero Divisor Graph for Modules
, 2019 Let R be a commutative ring with identity and M be an R-module. The zero divisor graph of M is denoted by Gamma(M). In this study, we are going to generalize the zero divisor graph Gamma(M) to submodule-based zero divisor graph Gamma(M, N) by replacing ...
Payrovi, Shiroyeh +2 more
core
The entire graph of a module with respect to a submodule
, 2019 In this paper, we introduce the entire graph of a module with respect to a submodule, as a generalization of the total graph of a commutative ring in the sense of Anderson–Badawi.
Masoumeh Shabani +2 more
core +1 more source
Class of Crosscap Two Graphs Arising from Lattices–I
, 2023 Let L be a lattice. The annihilating-ideal graph of L is a simple graph whose vertex set is the set of all nontrivial ideals of L and whose two distinct vertices I and J are adjacent if and only if I∧J=0.
Jehan A. Al-Bar +3 more
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On the genus and crosscap of the extended sum annihilating-ideal graph of commutative rings
In the context of a commutative ring with unity, denoted as S, and its associated set of annihilating ideals A(S), there exists a graph known as the extended sum annihilating-ideal graph, denoted as AGΩ(S).
Nazim +4 more
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Some Remarks on the Annihilating-Ideal Graph of Commutative Ring with Respect to an Ideal [PDF]
The graph $ AG ( R ) $ {of} a commutative ring $R$ with identity has an edge linking two unique vertices when the product of the vertices equals {the} zero ideal and its vertices are the nonzero annihilating ideals of $R$.The annihilating-ideal graph ...
Mohammad Hasan Naderi +1 more
core +1 more source
On the Genus of the Co-Annihilating Graph of Commutative Rings
, 2019 Let R be a commutative ring with identity and R be the set of all nonzero non-units of R. The co-annihilating graph of R, denoted by R, is a graph with vertex set R and two vertices x and y are adjacent whenever ann(x) ∩ ann(y) = (0).
Selvakumar, K. +3 more
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RINGS WHOSE ANNIHILATING-IDEAL GRAPHS HAVE POSITIVE GENUS
, 2012 Let R be a commutative ring and 𝔸(R) be the set of ideals with nonzero annihilators. The annihilating-ideal graph of R is defined as the graph 𝔸𝔾(R) with the vertex set 𝔸(R)* = 𝔸\{(0)} and two distinct vertices I and J are adjacent if and only if IJ = (0)
F. ALINIAEIFARD, M. BEHBOODI
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Classifying Annihilating-Ideal Graphs of Commutative Artinian Rings
, 2018 In this article we investigate the annihilating-ideal graph of a commutative ring, introduced by Behboodi and Rakeei in [BR11a]. Our main goal is to determine which algebraic properties of a ring are reflected in its annihilating-ideal graph.
Diesl, Alexander J. +2 more
core
, 2019 LetS be an assosiative ring with identitiy and N be a right S-module. We definethe non-maximal graph m(N) of N with all non-trivial submodules of N as verticesand two distinct vertices A,B areadjecent if and only if A + B is not maximal submodule of N ...
Tahire ÖZEN +3 more
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Some remarks on the dominating sets of the annihilating-ideal graph of a commutative ring
The rings considered in this article are commutative with identity which admit at least one nonzero annihilating ideal. Let $R$ be a ring. Let $\mathbb{A}(R)$ denote the set of all annihilating ideals of $R$ and let us denote $\mathbb{A}(R)\backslash ...
Subramanian Visweswaran +1 more
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