Affiliation:
1. Department of Mathematics , Shaanxi University of Science and Technology , Xi’an , Shaanxi , China
2. Department of Mathematics , Fasa University , Fasa , Iran
Abstract
Abstract
Let S be a pomonoid. In this paper, we introduce some new types of epimorphisms with certain purity conditions, and obtain equivalent descriptions of various flatness properties of S-posets, such as strong flatness, Conditions (E), (E′), (P), (P
w
), (WP), (WP)
w
, (PWP) and (PWP)
w
. Thereby, we present other equivalent conditions in the Stenström-Govorov-Lazard theorem for S-posets. Furthermore, we prove that these new epimorphisms are closed under directed colimits. Meantime, this implies that by a new approach we can show that most of flatness properties of S-posets can be transferred to their directed colimit. Finally, we prove that every class of S-posets having a flatness property is closed under directed colimits.
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