Authors | H. Barzegar, M.M. Ebrahimi |
---|---|
Journal | European journal of pure and applied mathematics |
Page number | 41-55 |
Serial number | 4 |
Volume number | 1 |
Paper Type | Original Research |
Published At | 2008 |
Journal Grade | Scientific - research |
Journal Type | Typographic |
Journal Country | Iran, Islamic Republic Of |
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 sequential purity, for
acts over semigroups (which is of some interest to computer scientists, too), and then show that it is
actually equivalent to Cp-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 sequentially pure monomorphisms. These properties are usually needed to study the
homological notions, such as injectivity, of acts.