Geodesic
A Note on Compactifying Artinian Rings
Canadian journal of mathematics, Tome 26 (1974) no. 3, pp. 580-582

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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. 
Haley, David K. A Note on Compactifying Artinian Rings. Canadian journal of mathematics, Tome 26 (1974) no. 3, pp. 580-582. doi: 10.4153/CJM-1974-054-2
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[1] 1. Haley, D. K., Equationally compact artinian rings, Can. J. Math. 25 (1973), 273–283. Google Scholar

[2] 2. Wenzel, G. H., On (, m)-atomic compact relational systems, Math. Ann. 134 (1971), 12–18. Google Scholar

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