TY - JOUR
ID - 10518
TI - Order dense injectivity of $S$-posets
JO - Categories and General Algebraic Structures with Applications
JA - CGASA
LA - en
SN - 2345-5853
AU - Shahbaz, Leila
AD - Department of Mathematics, University of Maragheh
Y1 - 2015
PY - 2015
VL - 3
IS - 1
SP - 43
EP - 63
KW - regular monomorphism
KW - order dense sub $S$-poset
KW - order dense injective
DO -
N2 - In 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.
UR - http://cgasa.sbu.ac.ir/article_10518.html
L1 - http://cgasa.sbu.ac.ir/article_10518_c47373537bc4095c9b7b11ef095abf14.pdf
ER -