@article {
author = {Haddadi, M. and Ebrahimi, M.M.},
title = {A radical extension of the category of $S$-sets},
journal = {Bulletin of the Iranian Mathematical Society},
volume = {43},
number = {5},
pages = {1153-1163},
year = {2017},
publisher = {Iranian Mathematical Society (IMS)},
issn = {1017-060X},
eissn = {1735-8515},
doi = {},
abstract = {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.},
keywords = {Radical,$S$-set,$S$-poset},
url = {http://bims.iranjournals.ir/article_1013.html},
eprint = {http://bims.iranjournals.ir/article_1013_e39fbaec4f209d34b2b2b5b8fbbd286c.pdf}
}