In this article, we give several generalizations of the concept of annihilating ideal graph over a commutative ring with identity to modules. Weobserve that over a commutative ring $R$, $Bbb{AG}_*(_RM)$ isconnected and diam$Bbb{AG}_*(_RM)leq 3$. Moreover, if $Bbb{AG}_*(_RM)$ contains a cycle, then $mbox{gr}Bbb{AG}_*(_RM)leq 4$. Also for an $R$-module $M$ with$Bbb{A}_*(M)neq S(M)setminus {0}$, $...

in this article, we give several generalizations of the concept of annihilating ideal graph over a commutative ring with identity to modules. weobserve that over a commutative ring $r$, $bbb{ag}_*(_rm)$ isconnected and diam$bbb{ag}_*(_rm)leq 3$. moreover, if $bbb{ag}_*(_rm)$ contains a cycle, then $mbox{gr}bbb{ag}_*(_rm)leq 4$. also for an $r$-module $m$ with$bbb{a}_*(m)neq s(m)setminus {0}$, $...

Let R be a commutative ring with unity, M unitary R-module and G finite abelian group (viewed as \({\mathbb {Z}}\)-module). The main objective of this paper is to study properties mod-annihilators M. For \(x \in M\), we the ideals \([x : M] =\{r\in ~|~ rM\subseteq Rx\}\) corresponding mod-annihilator We investigate when [x an essential ideal R. prove that arbitrary intersection represented by i...

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...

Let OX (resp. DX) be the sheaf of holomorphic functions (resp. the sheaf of linear differential operators with holomorphic coefficients) on X = C. Let D ⊂ X be a locally weakly quasi-homogeneous free divisor defined by a polynomial f . In this paper we prove that, locally, the annihilating ideal of 1/f over DX is generated by linear differential operators of order 1 (for k big enough). For this...

For an affine Lie algebra ĝ, the coefficients of certain vertex operators that annihilate level k standard ĝ-modules are defining relations for modules. In this paper, we study a combinatorial structure leading terms these = 2 algebras type Cn(1) and main result is construction combinatorially parameterized among annihilating fields. It believed constructed will play key role in Gröbner-like ba...

Let G be a digraph with n vertices and A(G) be its adjacency matrix. A monic polynomial f(x) of degree at most n is called an annihilating polynomial of G if f(A(G)) = 0. G is said to be annihilatingly unique if it possesses a unique annihilating polynomial. In this paper, the directed windmill M3(r) is defined and we study the annihilating uniqueness of M3(r).