Axiomatizability and completeness of the class of injective acts over a commutative monoid or a group
A. A. Stepanova · Siberian Mathematical Journal · 2015
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.