7 research outputs found
Independent sets of some graphs associated to commutative rings
Let be a simple graph. A set is independent set of
, if no two vertices of are adjacent. The independence number
is the size of a maximum independent set in the graph. %An
independent set with cardinality Let be a commutative ring with nonzero
identity and an ideal of . The zero-divisor graph of , denoted by
, is an undirected graph whose vertices are the nonzero
zero-divisors of and two distinct vertices and are adjacent if and
only if . Also the ideal-based zero-divisor graph of , denoted by
, is the graph which vertices are the set {x\in R\backslash I |
xy\in I \quad for some \quad y\in R\backslash I\} and two distinct vertices
and are adjacent if and only if . In this paper we study the
independent sets and the independence number of and .Comment: 27 pages. 22 figure
Transitivity of The delta^n-Relation in Hypergroups
The -relation was introduced by Leoreanu-Fotea et. al.\cite{130}. In this article, we introduce the concept of-heart of a hypergroup and we determine necessary andsufficient conditions for the relation to betransitive. Moreover, we determine a family ofsubsets of a hypergroup and we give sufficient conditionssuch that the geometric space is stronglytransitive and the relation is transitive
The construction of fractions of -module over commutative -ring
The aim of this paper is to construct fraction of -module over commutative -ring. There should be an appropriate set of elements in a -ring to be used as -module of fractions. Then we study the homomorphisms of -module which can lead to related basic results. We show that for every -module , Also, if is a finitely generated -module, then is finitely generated
Transitivity of the Delta^n-Relation in Hypergroups
The -relation was introduced by Leoreanu-Fotea et. al.\cite{130}. In this article, we introduce the concept of-heart of a hypergroup and we determine necessary andsufficient conditions for the relation to betransitive. Moreover, we determine a family ofsubsets of a hypergroup and we give sufficient conditionssuch that the geometric space is stronglytransitive and the relation is transitive
Generalization of Pawlak’s Approximations in Hypermodules by Set-Valued Homomorphisms
The initiation and majority on rough sets for algebraic hyperstructures such as hypermodules over a hyperring have been concentrated on a congruence relation. The congruence relation, however, seems to restrict the application of the generalized rough set model for algebraic sets. In this paper, in order to solve this problem, we consider the concept of set-valued homomorphism for hypermodules and we give some examples of set-valued homomorphism. In this respect, we show that every homomorphism of the hypermodules is a set-valued homomorphism. The notions of generalized lower and upper approximation operators, constructed by means of a set-valued mapping, which is a generalization of the notion of lower and upper approximations of a hypermodule, are provided. We also propose the notion of generalized lower and upper approximations with respect to a subhypermodule of a hypermodule discuss some significant properties of them