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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
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
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
Linking options:
https://www.mathnet.ru/eng/smj2667 https://www.mathnet.ru/eng/smj/v56/i3/p650
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