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 -