Shahrood University of Technology Journal of Algebraic Systems 2345-5128 5 2 2018 01 01 SEQUENTIALLY COMPACT S-ACTS 111 125 1095 10.22044/jas.2017.4357.1218 EN H. Barzegar Department of Mathematics, University of Tafresh , 3951879611, Tafresh, Iran. Journal Article 2016 05 21 ‎‎The investigation of equational compactness was initiated by‎<br /> ‎Banaschewski and Nelson‎. ‎They proved that pure injectivity is‎<br /> ‎equivalent to equational compactness‎. ‎Here we define the so‎<br /> ‎called sequentially compact acts over semigroups and study‎<br /> ‎some of their categorical and homological properties‎. ‎Some‎<br /> ‎Baer conditions for injectivity of S-acts are also presented‎. sequentially compact‎ ‎ ‎$f$-pure‎ ‎injective injective S-act https://jas.shahroodut.ac.ir/article_1095_09001f39c3743b6d98c90f11286807eb.pdf