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

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, University of Maragheh, 55181, Maragheh, Iran

    Leila Shahbaz

  2. Department of Mathematics, Shahid Beheshti University, G.C., 19839, Tehran, Iran

    Mojgan Mahmoudi

Authors
  1. Leila Shahbaz
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  2. Mojgan Mahmoudi
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Correspondence to Leila Shahbaz.

Additional information

Communicated by Benjamin Steinberg.

Dedicated to Professor M. Mehdi Ebrahimi on his 65th Birthday.

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Shahbaz, L., Mahmoudi, M. Injectivity of \(S\)-posets with respect to down closed regular monomorphisms. Semigroup Forum 91, 584–600 (2015). https://doi.org/10.1007/s00233-014-9676-y

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  • DOI: https://doi.org/10.1007/s00233-014-9676-y

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