scholarly journals Annihilator graphs of MV-algebras

2020 ◽  
pp. 2150188
Author(s):  
Aiping Gan ◽  
Yichuan Yang
Keyword(s):  
Zero Divisor ◽  
Spanning Subgraph ◽  
Zero Divisor Graph ◽  
Mv Algebra ◽  
Annihilator Graph ◽  
Mv Algebras

In this paper, we introduce the annihilator graph [Formula: see text] of an MV-algebra [Formula: see text]. We show that [Formula: see text] contains the zero-divisor graph [Formula: see text] as a spanning subgraph. We then prove that [Formula: see text] if and only if [Formula: see text]. Moreover, we obtain that the girth [Formula: see text].

scholarly journals Sub-semigroups determined by the zero-divisor graph

2008 ◽  
Vol 308 (22) ◽  
pp. 5122-5135 ◽  
Author(s):  
Tongsuo Wu ◽  
Dancheng Lu
Keyword(s):  
Zero Divisor ◽  
Zero Divisor Graph

ON RINGS R WHOSE GRAPHS Γ(R) SATISFY CONDITION (Kp)

2011 ◽  
Vol 10 (04) ◽  
pp. 665-674
Author(s):  
LI CHEN ◽  
TONGSUO WU
Keyword(s):  
Prime Number ◽  
Commutative Ring ◽  
Complete Graph ◽  
Zero Divisor ◽  
Commutative Rings ◽  
Satisfy Condition ◽  
Induced Subgraph ◽  
Zero Divisor Graph ◽  
Ring Graph ◽  
Finite Commutative Rings

Let p be a prime number. Let G = Γ(R) be a ring graph, i.e. the zero-divisor graph of a commutative ring R. For an induced subgraph H of G, let CG(H) = {z ∈ V(G) ∣N(z) = V(H)}. Assume that in the graph G there exists an induced subgraph H which is isomorphic to the complete graph Kp-1, a vertex c ∈ CG(H), and a vertex z such that d(c, z) = 3. In this paper, we characterize the finite commutative rings R whose graphs G = Γ(R) have this property (called condition (Kp)).

scholarly journals Zero Divisor Graph for the Ring of Eisenstein Integers Modulo n

Algebra ◽  
2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Osama Alkam ◽  
Emad Abu Osba
Keyword(s):  
Zero Divisor ◽  
Zero Divisor Graph

Let En be the ring of Eisenstein integers modulo n. In this paper we study the zero divisor graph Γ(En). We find the diameters and girths for such zero divisor graphs and characterize n for which the graph Γ(En) is complete, complete bipartite, bipartite, regular, Eulerian, Hamiltonian, or chordal.

Radical of a-Ideals in Mv -Modules

2014 ◽  
Vol 0 (0) ◽  
Author(s):  
F. Forouzesh ◽  
E. Eslami ◽  
A. Borumand Saeid
Keyword(s):  
Maximal Ideal ◽  
The Other ◽  
Subject Classification ◽  
Mv Algebra ◽  
Mv Algebras

Abstract In this paper, we introduce the notion of the radical of an ideal in MV - algebras. Several characterizations of this radical is given. We define the notion of a semi-maximal ideal in an MV -algebra and prove some theorems which give relations between this semi-maximal ideal and the other types of ideals in MV -algebras. Also we prove that A/I is a semi-simple MV -algebra if and only if I is a semi-maximal ideal of an MV -algebra A. The above notions are used to define the radical of A-ideals in MV -modules and investigate some properties. Mathematics Subject Classification 2010: 03B50, 03G25, 06D35

A generalized ideal-based zero-divisor graph

2015 ◽  
Vol 14 (06) ◽  
pp. 1550079 ◽  
Author(s):  
M. J. Nikmehr ◽  
S. Khojasteh
Keyword(s):  
Prime Ideal ◽  
Commutative Ring ◽  
Chromatic Number ◽  
Zero Divisor ◽  
Undirected Graph ◽  
Clique Number ◽  
Proper Ideal ◽  
Graph Structure ◽  
Zero Divisor Graph ◽  
Vertex Set

Let R be a commutative ring with identity, I its proper ideal and M be a unitary R-module. In this paper, we introduce and study a kind of graph structure of an R-module M with respect to proper ideal I, denoted by ΓI(RM) or simply ΓI(M). It is the (undirected) graph with the vertex set M\{0} and two distinct vertices x and y are adjacent if and only if [x : M][y : M] ⊆ I. Clearly, the zero-divisor graph of R is a subgraph of Γ0(R); this is an important result on the definition. We prove that if ann R(M) ⊆ I and H is the subgraph of ΓI(M) induced by the set of all non-isolated vertices, then diam (H) ≤ 3 and gr (ΓI(M)) ∈ {3, 4, ∞}. Also, we prove that if Spec (R) and ω(Γ Nil (R)(M)) are finite, then χ(Γ Nil (R)(M)) ≤ ∣ Spec (R)∣ + ω(Γ Nil (R)(M)). Moreover, for a secondary R-module M and prime ideal P, we determine the chromatic number and the clique number of ΓP(M), where ann R(M) ⊆ P. Among other results, it is proved that for a semisimple R-module M with ann R(M) ⊆ I, ΓI(M) is a forest if and only if ΓI(M) is a union of isolated vertices or a star.

Effect-like algebras induced by means of basic algebras

2010 ◽  
Vol 60 (1) ◽  
Author(s):  
Ivan Chajda
Keyword(s):  
Distributive Lattice ◽  
Effect Algebra ◽  
Binary Operation ◽  
Basic Algebra ◽  
Natural Question ◽  
Lattice Effect Algebra ◽  
Mv Algebra ◽  
Lattice Effect ◽  
Mv Algebras

AbstractHaving an MV-algebra, we can restrict its binary operation addition only to the pairs of orthogonal elements. The resulting structure is known as an effect algebra, precisely distributive lattice effect algebra. Basic algebras were introduced as a generalization of MV-algebras. Hence, there is a natural question what an effect-like algebra can be reached by the above mentioned construction if an MV-algebra is replaced by a basic algebra. This is answered in the paper and properties of these effect-like algebras are studied.

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