Research Article

Preenveloping classes of acts

Published in: Quaestiones Mathematicae
Volume 45 , issue 11 , 2022 , pages: 1739–1742

DOI: 10.2989/16073606.2021.1969604

Author(s): Mohanad Farhan Hamid University of Technology-Iraq, Iraq

Keywords: Primary: 20M30 , Secondary: 20M50 , Pure subact , preenvelope , absolutely pure act , weakly f-injective act , weakly p-injective act

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Abstract

Preenvelopes of acts over a monoid are defined by analogy with Enochs’ definition of preenvelopes of modules. Provided that it is closed for pure subacts, a class of acts is shown to be preenveloping precisely when it is closed under direct products. Examples of such classes include absolutely pure, weakly f-injective and weakly p-injective acts.

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