Centrally essential factor rings and subdirect indecomposability

Abstract

Let R be a ring and J(R), C(R) its Jacobson radical and center. If R is a centrally essential (CE ring for brevity) ring with R / J ( R ) commutative, then any minimal right ideal is contained in C(R). In a CE ring, every minimal right or left ideal is an ideal. A right Artinian (subdirectly indecomposable (SI, for brevity) right Noetherian) CE ring is an Artinian (a local Artinian) ring. R is duo if all factor rings of R are CE. We describe Noetherian SI CE rings and CE rings with SI center. We give examples of non-commutative SI CE rings.