A Note on Compactifying Artinian Rings
- 1 June 1974
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 26 (3) , 580-582
- https://doi.org/10.4153/cjm-1974-054-2
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.Keywords
This publication has 2 references indexed in Scilit:
- Equationally Compact Artinian RingsCanadian Journal of Mathematics, 1973
- On $${\text{(}}\mathfrak{S}, \mathfrak{U}, \mathfrak{m}{\text{)}}$$ -atomic compact relational systemsMathematische Annalen, 1971