%0 Journal Article
%T COGENERATOR AND SUBDIRECTLY IRREDUCIBLE IN THE CATEGORY OF S-POSETS
%J Journal of Algebraic Systems
%I Shahrood University of Technology
%Z 2345-5128
%A Moghaddasi, Gh.
%D 2015
%\ 02/01/2015
%V 2
%N 2
%P 137-146
%! COGENERATOR AND SUBDIRECTLY IRREDUCIBLE IN THE CATEGORY OF S-POSETS
%K S-poset
%K cogenerator
%K regular injective
%K subdirectly irreducible
%R 10.22044/jas.2015.371
%X In this paper we study the notions of cogenerator and subdirectly irreducible in the category of S-poset. First we give somenecessary and sufficient conditions for a cogenerator $S$-posets. Then we see that under some conditions, regular injectivity implies generator and cogenerator. Recalling Birkhoff's Representation Theorem for algebra, we study subdirectly irreducible S-posets and give this theorem for the category of ordered right acts over an ordered monoid. Among other things, we give the relations between cogenerators and subdirectly irreducible S-posets.
%U https://jas.shahroodut.ac.ir/article_371_cf285a5a87885ed211e1f128762fbc2f.pdf