Document Type : Research Note
Department of Mathematics, University of Tafresh , 3951879611, Tafresh, Iran.
The investigation of equational compactness was initiated by
Banaschewski and Nelson. They proved that pure injectivity is
equivalent to equational compactness. Here we define the so
called sequentially compact acts over semigroups and study
some of their categorical and homological properties. Some
Baer conditions for injectivity of S-acts are also presented.