A Note on Compactifying Artinian Rings

Abstract

In this note a number of compactifications are discussed within the class of artinian rings. In [1] the following was proved:Theorem. For an artinian ring R the following are equivalent:(1) R is equationally compact.(2) R+ ≃ B ⊕ P, where B is a finite group, P is a finite direct sum of Prüfer groups, and R · P = P · R = {0}.(3) R is a retract of a compact topological ring.