TY - JOUR ID - 1013 TI - A radical extension of the category of $S$-sets JO - Bulletin of the Iranian Mathematical Society JA - BIMS LA - en SN - 1017-060X AU - Haddadi, M. AU - Ebrahimi, M.M. AD - Faculty of Mathematics, Statistics and Computer Sciences, Department of Mathematics, Semnan University, Semnan, Iran. AD - Department of Mathematics, Shahid Beheshti University, Tehran 19839, Iran. Y1 - 2017 PY - 2017 VL - 43 IS - 5 SP - 1153 EP - 1163 KW - Radical‎ KW - ‎$S$-set‎ KW - ‎$S$-poset‎ DO - N2 - 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. UR - http://bims.iranjournals.ir/article_1013.html L1 - http://bims.iranjournals.ir/article_1013_e39fbaec4f209d34b2b2b5b8fbbd286c.pdf ER -