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Modules of existentially closed algebras

Published online by Cambridge University Press:  12 March 2014

Paul C. Eklof  and
Hans-Christian Mez
Paul C. Eklof
Affiliation:
Department of Mathematics, University of California, Irvine, California 92717
Hans-Christian Mez*
Affiliation:
Department of Mathematics, University of California, Berkeley, California 94720
*
Carl-Maria v. Weberstr. 1, D-7800 Freiburg, West Germany
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Abstract

The underlying modules of existentially closed ⊿-algebras are studied. Among other things, it is proved that they are all elementarily equivalent, and that all of them are existentially closed as modules if and only if ⊿ is regular. It is also proved that every saturated module in the appropriate elementary equivalence class underlies an ex. ⊿-algebra. Applications to some problems in module theory are given. A number of open questions are mentioned.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 52 , Issue 1 , March 1987 , pp. 54 - 63
Copyright
Copyright © Association for Symbolic Logic 1987

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Footnotes

1

Partially supported by NSF grant DSM-8400451

References

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