We propose a efficient method to calculate “the minimal annihilating polynomials” for all the unit vectors, of square matrix over the integers or the rational numbers. The minimal annihilating polynomials are useful for improvement of efficiency in wide variety of algorithms in exact linear algebra. We propose a efficient algorithm for calculating the minimal annihilating polynomials for all th...

the rings considered in this article are  commutative  with identity which admit at least two  nonzero annihilating ideals. let $r$ be a ring. let $mathbb{a}(r)$ denote the set of all annihilating ideals of $r$ and let $mathbb{a}(r)^{*} = mathbb{a}(r)backslash {(0)}$. the annihilating-ideal graph of $r$, denoted by $mathbb{ag}(r)$  is an undirected simple graph whose vertex set is $mathbb{a}(r)...

Let R be a commutative ring with identity and A(R) be the set of ideals with nonzero annihilator. The annihilating-ideal graph of R is defined as the graph AG(R) with the vertex set A(R) = A(R)r {0} and two distinct vertices I and J are adjacent if and only if IJ = 0. In this paper, we study the domination number of AG(R) and some connections between the domination numbers of annihilating-ideal...

Let R be a non-domain commutative ring with identity and A(R) be theset of non-zero ideals with non-zero annihilators. We call an ideal I of R, anannihilating-ideal if there exists a non-zero ideal J of R such that IJ = (0).The annihilating-ideal graph of R is defined as the graph AG(R) with the vertexset A(R) and two distinct vertices I and J are adjacent if and only if IJ =(0). In this paper,...

The annihilating-ideal graph of a commutative ring $R$ is denoted by $AG(R)$, whose vertices are all nonzero ideals of $R$ with nonzero annihilators and two distinct vertices $I$ and $J$ are adjacent if and only if $IJ=0$. In this article, we completely characterize rings $R$ when $gr(AG(R))neq 3$.