Injectivity of \(S\) -posets with respect to down closed regular monomorphisms

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• 作者：Leila Shahbaz ; Mojgan Mahmoudi
• 关键词：$$S$$ S ; poset ; Down closed sub $$S$$ S ; poset ; dc ; injective
• 刊名：Semigroup Forum
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：91
• 期：3
• 页码：584-600
• 全文大小：442 KB
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• 作者单位：Leila Shahbaz (1)
  Mojgan Mahmoudi (2)
  
  1. Department of Mathematics, University of Maragheh, 55181, Maragheh, Iran
  2. Department of Mathematics, Shahid Beheshti University, G.C., 19839, Tehran, Iran
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Algebra
  
• 出版者：Springer New York
• ISSN：1432-2137

文摘

No need to say that the study of injectivity with respect to different classes of monomorphisms is crucial in any category. In this paper, the notion of injectivity with respect to down closed 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 down closed injectivity. Also, we consider such injectivity for \(S\) itself, and its (po)ideals. Further, we investigate if this kind of injectivity is preserved or reflected by products, coproducts, direct sums, and order sums of \(S\)-posets. Finally, we define and study some kinds of weak injectivity with respect to down closed embeddings. Keywords \(S\)-poset Down closed sub \(S\)-poset dc-injective