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Sibirskii Matematicheskii Zhurnal, 2015, Volume 56, Number 3, Pages 650–662
DOI: https://doi.org/10.17377/smzh.2015.56.315 (Mi smj2667) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Axiomatizability and completeness of the class of injective acts over a commutative monoid or a group

A. A. Stepanovaab

a Far Eastern Federal University, Vladivostok, Russia
b Institute for Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences, Vladivostok, Russia
Full-text PDF (337 kB) Citations (4)
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DOI: https://doi.org/10.17377/smzh.2015.56.315
Abstract: We study monoids $S$ over which the class of injective $S$-acts is axiomatizable, complete, and model complete. We prove that, for a countable commutative monoid or a countable group $S$, the class of injective $S$-acts is axiomatizable if and only if $S$ is a finitely generated monoid. We show that there is no nontrivial monoid nor a group the class of injective acts over which is complete, model complete, or categorical.
Keywords: axiomatizable class, complete class, model complete class, categorical class, act, injective act.
Received: 15.09.2014
English version:
Siberian Mathematical Journal, 2015, Volume 56, Issue 3, Pages 516–525
DOI: https://doi.org/10.1134/S0037446615030155
Bibliographic databases:
Document Type: Article
UDC: 510.67+512.56
Language: Russian
Citation: A. A. Stepanova, “Axiomatizability and completeness of the class of injective acts over a commutative monoid or a group”, Sibirsk. Mat. Zh., 56:3 (2015), 650–662; Siberian Math. J., 56:3 (2015), 516–525
Citation in format AMSBIB
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Сибирский математический журнал Siberian Mathematical Journal
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