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Leila Shahbaz

Leila Shahbaz

Academic rank: Associate Professor
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Education: PhD.
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Faculty: 1
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Research

Title
Order dense injectivity of S-posets
Type
JournalPaper
Keywords
regular monomorphism, order dense sub S-poset, order dense injective
Year
2015
Journal Categories and General Algebraic Structures with Applications
DOI
Researchers Leila Shahbaz

Abstract

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.