Sequentially pure monomorphisms of acts over semigroups
Keywords:
Action of a semigroup, purityAbstract
Any notion of purity is normally defined in terms of
solvability of some set of equations. In this paper we first take
 this point of view to introduce a kind of purity, called
$s$-purity, for acts over semigroups (which is of some interest
to computer scientists), and then show that it is actually
equivalent to $C^p$-purity resulting from a closure operator.
The main objective of the paper is to study properties of the
category of all acts over a semigroup with respect to $C^p$-pure
monomorphisms. These properties are needed to study the
homological notions, such as injectivity, of acts. given
act.
Downloads
Published
Issue
Section
License
Upon acceptance of an article by the European Journal of Pure and Applied Mathematics, the author(s) retain the copyright to the article. However, by submitting your work, you agree that the article will be published under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0). This license allows others to copy, distribute, and adapt your work, provided proper attribution is given to the original author(s) and source. However, the work cannot be used for commercial purposes.
By agreeing to this statement, you acknowledge that:
- You retain full copyright over your work.
- The European Journal of Pure and Applied Mathematics will publish your work under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).
- This license allows others to use and share your work for non-commercial purposes, provided they give appropriate credit to the original author(s) and source.