Journal of Symbolic Logic

Modules of Existentially Closed Algebras

Paul C. Eklof and Hans-Christian Mez

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Abstract

The underlying modules of existentially closed $\triangle$-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 $\triangle$ is regular. It is also proved that every saturated module in the appropriate elementary equivalence class underlies an e.c. $\triangle$-algebra. Applications to some problems in module theory are given. A number of open questions are mentioned.

Article information

Source
J. Symbolic Logic, Volume 52, Issue 1 (1987), 54-63.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183742309

Mathematical Reviews number (MathSciNet)
MR877854

Zentralblatt MATH identifier
0629.03011

JSTOR
links.jstor.org

Citation

Eklof, Paul C.; Mez, Hans-Christian. Modules of Existentially Closed Algebras. J. Symbolic Logic 52 (1987), no. 1, 54--63. https://projecteuclid.org/euclid.jsl/1183742309


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