Model theoretic properties of free, projective and flat acts

Victoria Gould; Alexander Mikhalev; Evgeny Palyutin; Alena Stepanova

Model theoretic properties of free, projective and flat acts

Victoria Gould, Alexander Mikhalev, Evgeny Palyutin, Alena Stepanova

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

This is the second in a series of articles surveying the body of work on the model theory of S-acts over a monoid S. The first concentrated on the theory of regular S-acts. Here we review the material on model-theoretic properties of free, projective, and (strongly, weakly) flat S-acts. We consider questions of axiomatizability, completeness, model completeness, and stability for these classes. Most but not all of the results have already appeared; we remark that the description of those monoids S such that the class of free left S-acts is axiomatizable, is new.

Original language	English
Pages (from-to)	63-110
Number of pages	48
Journal	Fund. Appl. Math.
Volume	14
Issue number	7
Publication status	Published - 1 Apr 2008

Keywords

Algebra, Pure Mathematics

Access to Document

http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=fpm&paperid=1174&option_lang=eng

Cite this

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N2 - This is the second in a series of articles surveying the body of work on the model theory of S-acts over a monoid S. The first concentrated on the theory of regular S-acts. Here we review the material on model-theoretic properties of free, projective, and (strongly, weakly) flat S-acts. We consider questions of axiomatizability, completeness, model completeness, and stability for these classes. Most but not all of the results have already appeared; we remark that the description of those monoids S such that the class of free left S-acts is axiomatizable, is new.

AB - This is the second in a series of articles surveying the body of work on the model theory of S-acts over a monoid S. The first concentrated on the theory of regular S-acts. Here we review the material on model-theoretic properties of free, projective, and (strongly, weakly) flat S-acts. We consider questions of axiomatizability, completeness, model completeness, and stability for these classes. Most but not all of the results have already appeared; we remark that the description of those monoids S such that the class of free left S-acts is axiomatizable, is new.

KW - Algebra, Pure Mathematics

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JO - Fund. Appl. Math.

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