Purity in the category of S-posets

نویسندگانH.Rasouli, H.Barzegar, L.Shahbaz
نشریهCommunication in Algebra
شماره صفحات5053-5067
شماره سریال12
شماره مجلد45
نوع مقالهFull Paper
تاریخ انتشار2017
رتبه نشریهعلمی - پژوهشی
نوع نشریهچاپی
کشور محل چاپبریتانیا

چکیده مقاله

In this paper, purity of S-posets over a pomonoid S is investigated.We rst study
some basic properties of absolutely po-pure S-posets. Among other results,
it is proved that every regular injective S-poset is absolutely po-pure, and
every absolutely po-pure inequationally compact S-poset is regular injective.
Then, using the notion of semi-nitely presented S-poset based on the nitely
induced S-poset congruence,we nd an equivalent condition for an S-poset to
be 1-po-pure in a regular extension. Finally, a characterization of an absolutely
1-po-pure S-poset is presented.