On Co-Maximal Subgroup Graph of a Group

The co-maximal subgroup graph $\Gamma(G)$ of a group $G$ is a graph whose vertices are non-trivial proper subgroups of $G$ and two vertices $H$ and $K$ are adjacent if $HK=G$. In this paper, we continue the study of $\Gamma(G)$, especially when $\Gamma(G)$ has isolated vertices. We define a new graph $\Gamma^*(G)$, which is obtained by removing isolated vertices from $\Gamma(G)$. We characterize when $\Gamma^*(G)$ is connected, a complete graph, star graph, has an universal vertex etc. We also find various graph parameters like diameter, girth, bipartiteness etc. in terms of properties of $G$.Comment: 14 pages, 3 figure

Single valued neutrosophic (M; n)-ideals of ordered Semirings

The aim of this paper is to combine the innovative concept of single valued neutrosophic sets and ordered semirings. It studies ordered semirings by the properties of their single valued neutrosphic subsets. In this regard, we define single valued neutrosophic (m; n)-ideals (SVN-(m; n)-ideals) of ordered semirings. First, we illustrate our new definition by non-trivial examples. Second, we study these SVN-(m; n)-ideals under different operations of SVNS. Finally, we find a relationship between the (m; n)-ideals of ordered semirings and level sets by finding a necessary and sufficient condition for an SVNS of an ordered semiring R to be an SVN-(m; n)-ideal of R

Ideal Graphs

In this dissertation, we explore various types of graphs that can be associated to a commutative ring with identity. In particular, if R is a commutative ring with identity, we consider a number of graphs with the vertex set being the set of proper ideals; various edge sets defined via different ideal theoretic conditions give visual insights and structure theorems pertaining to the multiplicative ideal theory of R. We characterize the interplay between the ideal theory and various properties of these graphs including diameter and connectivity

On graded AA-2-absorbing submodules of graded modules over graded commutative rings

Let $G$ be a group with identity $e$. Let $R$ be a $G$-graded commutative ring, $M$ a graded $R$-module and $A\subseteq h(R)$ a multiplicatively closed subset of $R$. In this paper, we introduce the concept of graded $A$-2-absorbing submodules of $M$ as a generalization of graded 2-absorbing submodules and graded $A$-prime submodules of $M.$ We investigate some properties of this class of graded submodules.Comment: arXiv admin note: text overlap with arXiv:2012.1360

Linear Diophantine Fuzzy Subspaces of a Vector Space

The notion of a linear diophantine fuzzy set as a generalization of a fuzzy set is a mathematical approach that deals with vagueness in decision-making problems. The use of reference parameters associated with validity and non-validity functions in linear diophantine fuzzy sets makes it more applicable to model vagueness in many real-life problems. On the other hand, subspaces of vector spaces are of great importance in many fields of science. The aim of this paper is to combine the two notions. In this regard, we consider the linear diophantine fuzzification of a vector space by introducing and studying the linear diophantine fuzzy subspaces of a vector space. First, we studied the behaviors of linear diophantine fuzzy subspaces of a vector space under a linear diophantine fuzzy set. Second, and by means of the level sets, we found a relationship between the linear diophantine fuzzy subspaces of a vector space and the subspaces of a vector space. Finally, we discuss the linear diophantine fuzzy subspaces of a quotient vector space

Linear Diophantine Fuzzy Subspaces of a Vector Space

The notion of a linear diophantine fuzzy set as a generalization of a fuzzy set is a mathematical approach that deals with vagueness in decision-making problems. The use of reference parameters associated with validity and non-validity functions in linear diophantine fuzzy sets makes it more applicable to model vagueness in many real-life problems. On the other hand, subspaces of vector spaces are of great importance in many fields of science. The aim of this paper is to combine the two notions. In this regard, we consider the linear diophantine fuzzification of a vector space by introducing and studying the linear diophantine fuzzy subspaces of a vector space. First, we studied the behaviors of linear diophantine fuzzy subspaces of a vector space under a linear diophantine fuzzy set. Second, and by means of the level sets, we found a relationship between the linear diophantine fuzzy subspaces of a vector space and the subspaces of a vector space. Finally, we discuss the linear diophantine fuzzy subspaces of a quotient vector space

Linear Diophantine Fuzzy Set Theory Applied to <i>BCK/BCI</i>-Algebras

In this paper, we apply the concept of linear Diophantine fuzzy sets in BCK/BCI-algebras. In this respect, the notions of linear Diophantine fuzzy subalgebras and linear Diophantine fuzzy (commutative) ideals are introduced and some vital properties are discussed. Additionally, characterizations of linear Diophantine fuzzy subalgebras and linear Diophantine fuzzy (commutative) ideals are considered. Moreover, the associated results for linear Diophantine fuzzy subalgebras, linear Diophantine fuzzy ideals and linear Diophantine fuzzy commutative ideals are obtained