Sequentially pure monomorphisms of acts over semigroups

Authors

  • Mohammad Mehdi Ebrahimi Professor
  • H Barzegar

Keywords:

Action of a semigroup, purity

Abstract

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.

Author Biographies

  • Mohammad Mehdi Ebrahimi, Professor
    Department of Mathematics, Shahid Beheshti University, Tehran 19839, Iran
  • H Barzegar
    Department of Mathematics, Shahid Beheshti University, Tehran 19839, Iran

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Published

2009-03-22

Issue

Section

Algebra

How to Cite

Sequentially pure monomorphisms of acts over semigroups. (2009). European Journal of Pure and Applied Mathematics, 1(4). https://www.ejpam.com/index.php/ejpam/article/view/97