عنوان مجله
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Categories and General Algebraic Structures with Applications
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چکیده
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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.
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