Shahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-58533120150701Order dense injectivity of $S$-posets436310518ENLeilaShahbazDepartment of Mathematics, University of MaraghehJournal Article20150822In this paper, the notion of injectivity with respect to order dense embeddings in the category of $S$-posets, posets with a monotone action of a pomonoid $S$ on them, is studied. We give a criterion, like the Baer condition for injectivity of modules, or Skornjakov criterion for injectivity of $S$-sets, for the order dense injectivity. Also, we consider such injectivity for $S$ itself, and its order dense ideals. Further, we define and study some kinds of weak injectivity with respect to order dense embeddings, consider their relations with order dense injectivity. Also investigate if these kinds of injectivity are preserved or reflected by products, coproducts, and direct sums of$S$-posets.http://cgasa.sbu.ac.ir/article_10518_c47373537bc4095c9b7b11ef095abf14.pdf