Modular annihilator algebras (Q1180749)

An element \(s\) belonging to the algebra \(A\) is called single if whenever \(asb=0\) for some \(a,b\) in \(A\) then at least either \(as\) or \(sb\) is zero. The purpose of this article is the study of single elements in modular annihilator algebras and how these elements are related to minimal left (right) ideals. The following is a typical result of this paper. Theorem: Let \(A\) be a semi-prime modular annihilator algebra and let \(s\) be a single elements of \(A\), \(s\bar\in \text{Rad }A\). Then the principal left ideal \(As\) is minimal.