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Pure-semisimplicity is preserved under elementary equivalence

Published online by Cambridge University Press:  18 May 2009

Maher Zayed
Maher Zayed
Affiliation:
Department of Mathematics, University of Bahrain, P.O. Box 32038, Isa Town, State of Bahrain
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In the present note, Σr denotes the class of all right pure semisimple rings (= right pure global dimension zero). It is known that if R ∈ Σr, then R is right artinian and every indecomposable right R-module is finitely generated. The class Σr is not closed under ultraproducts [4]. While Σr is closed under elementary descent (i.e. if S ∈ Σr and R is an elementary subring of S then R ∈ σr) [4], it is an open question whether right pure-semisimplicity is preserved under the passage to ultrapowers [4, Prob. 11.16]. In this note, this question is answered in the affirmative.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 36 , Issue 3 , September 1994 , pp. 345 - 346
Copyright
Copyright © Glasgow Mathematical Journal Trust 1994

References

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