TY - JOUR ID - 1764 TI - A NEW CHARACTERIZATION OF ABSOLUTELY PO-PURE AND ABSOLUTELY PURE S-POSETS JO - Journal of Algebraic Systems JA - JAS LA - en SN - 2345-5128 AU - Khosravi, R. AU - Roueentan, M. AD - Department of Mathematics, Faculty of Sciences, Fasa University, P.O. Box: 74617- 81189, Fasa, Iran. AD - Lamerd Higher Education Center, Lamerd, Iran. Y1 - 2020 PY - 2020 VL - 8 IS - 1 SP - 27 EP - 37 KW - S-posets KW - pomonoids KW - absolutely po-pure KW - 1-po-pure KW - regular injective DO - 10.22044/jas.2019.8295.1403 N2 - In this paper, we investigate po-purity using finitely presented S-posets, and give some equivalent conditions under which an S-poset is absolutely po-pure. We also introduce strongly finitely presented S-posets to characterize absolutely pure S-posets. Similar to the acts, every finitely presented cyclic S-posets is isomorphic to a factor S-poset of a pomonoid S by a finitely generated right congruence on S. Finally, the relationships between regular injectivity and absolute po-purity are considered. UR - https://jas.shahroodut.ac.ir/article_1764.html L1 - https://jas.shahroodut.ac.ir/article_1764_19902decb3c6a41c0cbf3f4368d348d7.pdf ER -