Ideal based trace graph of matrices

Exact annihilating-ideal graph of commutative rings

The rings considered in this article are commutative rings with identity $1neq 0$. The aim of this article is to define and study the exact annihilating-ideal graph of commutative rings. We discuss the interplay between the ring-theoretic properties of a ring and graph-theoretic properties of exact annihilating-ideal graph of the ring.

Properties of extended ideal based zero divisor graph of a commutative ring

This paper deals with some results concerning the notion of extended ideal based zero divisor graph $overline Gamma_I(R)$ for an ideal $I$ of a commutative ring $R$ and characterize its bipartite graph. Also, we study the properties of an annihilator of $overline Gamma_I(R)$.

Existence of Ideal matrices

An m×n ideal matrix is a periodic m×n binary matrix which satisfies the following two conditions: (1) each column of this matrix contains precisely one 1 and (2) if it is visualized as a dot pattern (with each dot representing a 1), then the number of overlapping dots at all actual shifts are 1 or 0. Let s(n) denote the smallest integer m such that an m × n ideal matrix exists. In this paper, w...

The principal ideal subgraph of the annihilating-ideal graph of commutative rings

Let $R$ be a commutative ring with identity and $mathbb{A}(R)$ be the set   of ideals of $R$ with non-zero annihilators. In this paper, we first introduce and investigate the principal ideal subgraph of the annihilating-ideal graph of $R$, denoted by $mathbb{AG}_P(R)$. It is a (undirected) graph with vertices $mathbb{A}_P(R)=mathbb{A}(R)cap mathbb{P}(R)setminus {(0)}$, where   $mathbb{P}(R)$ is...

IDEAL MATRICES . Ill