Let $R$ be a commutative ring with identity. Let $G(R)$ denote the maximal graph associated to $R$, i.e., $G(R)$ is a graph with vertices as the elements of $R$, where two distinct vertices $a$ and $b$ are adjacent if and only if there is a maximal ideal of $R$ containing both. Let $Gamma(R)$ denote the restriction of $G(R)$ to non-unit elements of $R$. In this paper we study the various graphi...

This paper presents the classication of invariant subgroups automorphism groups regular elements obtained from nite local near-rings, appropriate algebraic structure to study non-linear functions on finite groups. Just as rings matrices operate vector spaces, near-rings In this paper, we construct classes zero symmetric near-ring characteristic pk; k = 1; 2 ; \(\ge\) 3 admitting frobenius deriv...

A construction procedure for planar near-rings is provided. Amongst others, this method will show why many planar near-rings come in pairs with “opposite” geometries and it will also lead to the construction of many new infinite circular planar near-rings.

Molodtsov introduced the theory of soft sets, which can be seen as an effective mathematical tool to deal with uncertainties, since it is free from the difficulties that the usual theoretical approaches have troubled. In this paper, we apply the definitions proposed by Ali et al. [M. I. Ali, F. Feng, X. Liu, W. K. Min and M. Shabir, On some new operations in soft set theory, Comput. Math. Appl....