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A Note on Compactifying Artinian Rings

Published online by Cambridge University Press:  20 November 2018

David K. Haley
David K. Haley*
Affiliation:
Universität Mannheim, Mannheim, West Germany
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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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 3 , June 1974 , pp. 580 - 582
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Haley, D. K., Equationally compact artinian rings, Can. J. Math. 25 (1973), 273–283.Google Scholar
2. Wenzel, G. H., On (, m)-atomic compact relational systems, Math. Ann. 134 (1971), 12–18.Google Scholar