A selection of maximal elements under non-transitive indifferences

When Non-transitive Relations have Maximal Elements and Competitive Equilibrium Can’t be Beat

Maximal subsets of pairwise non-commuting elements of some finite p-groups

Let G be a group. A subset X of G is a set of pairwise noncommuting elements if xy ̸= yx for any two distinct elements x and y in X. If |X| ≥ |Y | for any other set of pairwise non-commuting elements Y in G, then X is said to be a maximal subset of pairwise non-commuting elements. In this paper we determine the cardinality of a maximal subset of pairwise non-commuting elements in any non-abelian...

A note on maximal non-prime ideals

The rings considered in this article are commutative with identity $1neq 0$. By a proper ideal of a ring $R$,  we mean an ideal $I$ of $R$ such that $Ineq R$.  We say that a proper ideal $I$ of a ring $R$ is a  maximal non-prime ideal if $I$ is not a prime ideal of $R$ but any proper ideal $A$ of $R$ with $ Isubseteq A$ and $Ineq A$ is a prime ideal. That is, among all the proper ideals of $R$,...

AUTOMORPHISM GROUPS OF SOME NON-TRANSITIVE GRAPHS

An Euclidean graph associated with a molecule is defined by a weighted graph with adjacency matrix M = [dij], where for ij, dij is the Euclidean distance between the nuclei i and j. In this matrix dii can be taken as zero if all the nuclei are equivalent. Otherwise, one may introduce different weights for distinct nuclei. Balaban introduced some monster graphs and then Randic computed complexit...

Maximal Elements of Support

We introduce a set that is tightly close to the set of the Jacobson radical of module (the intersection of all maximal elements in support). In the last section, it is proved that the set of zero divisors of a module is equal to the union of the maximal elements of the support of module if the module is finitely generated and injective.