The EA-Dimension of a Commutative Ring

Abstract

An elementary annihilator of a ring is an annihilator that has the form (0 : ) ; ∈ \ (0). We define the elementary annihilator dimension of the ring , denoted by EAdim( ), to be the upper bound of the set of all integers such that there is a chain (0 : 0 ) ⊂ ⋅ ⋅ ⋅ ⊂ (0 : ) of annihilators of . We use this dimension to characterize some zero-divisors graphs.