%0 Journal Article
%T A radical extension of the category of $S$-sets
%J Bulletin of the Iranian Mathematical Society
%I Iranian Mathematical Society (IMS)
%Z 1017-060X
%A Haddadi, M.
%A Ebrahimi, M.M.
%D 2017
%\ 10/31/2017
%V 43
%N 5
%P 1153-1163
%! A radical extension of the category of $S$-sets
%K Radical
%K $S$-set
%K $S$-poset
%R
%X Let S-Set be the category of $S$-sets, sets together with the actions of a semigroup $S$ on them. And, let S-Pos be the category of $S$-posets, posets together with the actions compatible with the orders on them. In this paper we show that the category S-Pos is a radical extension of S-Set; that is there is a radical on the category S-Pos, the order desolator radical, whose torsion-free class is S-Set. To do this, first we give a precise definition of a radical on the category S-Posand construct some functors between the above mentioned categories and finally we show that S-Pos is a radical extension of S-Set.
%U http://bims.iranjournals.ir/article_1013_e39fbaec4f209d34b2b2b5b8fbbd286c.pdf