This article is cited in 4 papers

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

A. A. Stepanova<sup>ab

a</sup> 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.

UDC: 510.67+512.56

Received: 15.09.2014

DOI: 10.17377/smzh.2015.56.315

 English version: Siberian Mathematical Journal, 2015, 56:3, 516–525

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