Let $R$ be a commutative ring and $I$ an ideal of $R$. The zero-divisor graph of $R$ with respect to $I$, denoted by $Gamma_I(R)$, is the simple graph whose vertex set is ${x in Rsetminus I mid xy in I$, for some $y in Rsetminus I}$, with two distinct vertices $x$ and $y$ are adjacent if and only if $xy in I$. In this paper, we state a relation between zero-divisor graph of $R$ with respec...

Let f1, . . . , fp be polynomials in C[x1, . . . , xn] and let D = Dn be the n-th Weyl algebra. We provide upper bounds for the complexity of computing the annihilating ideal of fs = f1 1 · · · f sp p in D[s] = D[s1, . . . , sp]. These bounds provide an initial explanation on the differences between the running times of the two methods known to obtain the so-called BernsteinSato ideals.

We describe an algorithm deciding if the annihilating ideal of the meromorphic function 1 f , where f = 0 defines an arrangement of hyperplanes, is generated by linear differential operators of order 1. The algorithm is based on the comparison of two characteristic cycles and uses a combinatorial description due to Àlvarez-Montaner, Garćıa–López and Zarzuela of the characteristic cycle of the D...

Let $G=(V,E)$ be a simple graph. A set $Ssubseteq V$ isindependent set of $G$,  if no two vertices of $S$ are adjacent.The  independence number $alpha(G)$ is the size of a maximumindependent set in the graph. In this paper we study and characterize the independent sets ofthe zero-divisor graph $Gamma(R)$ and ideal-based zero-divisor graph $Gamma_I(R)$of a commutative ring $R$.

abstract. let $l$ be a lattice with the least element $0$. an element $xin l$ is a zero divisor if $xwedge y=0$ for some $yin l^*=lsetminus left{0right}$. the set of all zero divisors is denoted by $z(l)$. we associate a simple graph $gamma(l)$ to $l$ with vertex set $z(l)^*=z(l)setminus left{0right}$, the set of non-zero zero divisors of $l$ and distinct $x,yin z(l)^*$ are adjacent if and only...