The EA-dimension of a commutative ring (Q2014901)

Summary: An elementary annihilator of a ring \(A\) is an annihilator that has the form \((0:a)_A\); \(a\in R\setminus (0)\). We define the elementary annihilator dimension of the ring \(A\), denoted by \(\mathrm{EAdim}(A)\), to be the upper bound of the set of all integers \(n\) such that there is a chain \((0:a_0)\subset\cdots\subset(0:a_n)\) of annihilators of \(A\). We use this dimension to characterize some zero-divisors graphs.