环的强零因子图的一个注记

一个环R的一个元α叫做一个强零因子，假如对R中的某个非零元b，有〈α〉〈b〉=0，或者〈b〉〈α〉=0（其中〈x〉是由x∈R生成的理想）．在该文中，用S（R）表示所有强零因子的集合．对于任意的一个环r，用^~Г（R）表示一个无向图，它的顶点集是S（R）^＊=S（R）-{0}，其中两上不同的顶点α和b相连当且仅当〈n〉〈b〉=0或者〈b〉〈α〉=0．该文主要研究质环直积的强零因子图的团数．

A Note on Strong Zero-divisor Graphs of Rings

An dement a in a ring R is caled a strong zero-divisor if either < a > < b > = 0 or < b > < a > = 0, for some 0≠b∈ R( < x > is the ideal generated by x∈ R ). Let S(R) denote the set of strong zero-divisors of R. The strong zero-divisor graph Γ(R) is an undirected graph with vertices S(R)* ( = S(R) - {0} ), where distinct vertices a and b are adjacent if and only if either < a > < b > = 0 or < b > < a > = 0. In this note, we study the number of cliques of the strong zero-divisor graph of a direct product of prime rings.