On Rees Factor S-Posets Satisfying Conditions (PWPE) or (PWPE)w

Document Type : Research Paper

Authors

Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran

Abstract

Golchin and Rezaei introduced conditions (PWP) and\linebreak (PWP)w in (Subpullbacks and flatness properties of S-posets). In this paper, we introduce conditions (PWPE) and (PWPE)w as generalizations of  these conditions, respectively, and show that the relevant implications are strict. In  general, we observe that condition (PWPE)w follows from condition (PWPE), but not conversely. Also, we prove that principal weak po-flatness follows from condition  (PWPE)w, but not conversely. Then, we obtain some general properties of conditions (PWPE) and (PWPE)w, and find sufficient and necessary conditions for the S-poset A(I) to satisfy these conditions.  Finally, we find conditions on a pomonoid S under which a cyclic or Rees factor S-poset satisfies condition (PWPE) or condition (PWPE)w. Thereby, we present some homological classifications of      pomonoids over which each of the conditions  (PWPE) and (PWPE)w implies a specific property, and vice versa, for Rees factor S-posets.

Keywords

References

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History

  • Receive Date: 17 May 2022
  • Revise Date: 02 October 2022
  • Accept Date: 23 February 2023

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