Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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On Generators in the Category of Actions of Pomonoids on Posets and its Slices

  • Farideh, Farsad (Department of Mathematics, Faculty of Mathematics, Statistics and Computer Science, Semnan University) ;
  • Ali, Madanshekaf (Department of Mathematics, Faculty of Mathematics, Statistics and Computer Science, Semnan University)
  • Received : 2021.11.29
  • Accepted : 2022.10.10
  • Published : 2022.12.31
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Abstract

Where S is a pomonoid, let Pos-S be the category of S-posets and S-poset maps. We start off by characterizing the pomonoids S for which all projectives in this category are either generators or free. We then study the notions of regular injectivity and weakly regularly d-injectivity in this category. This leads to homological classification results for pomonoids. Among other things, we get find relationships between regular injectivity in the slice category Pos-S/BS, for any S-poset BS, and generators and cyclic projectives in Pos-S.

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Acknowledgement

The authors would like to express their sincere thanks to the anonymous referee for a careful reading of the manuscript and for invaluable comments which improved the exposition of the article. Parts of this research were completed while the second author was on sabbatical leave at the Department of Mathematics, Vanderbilt University (VU), Nashvile, TN, USA. This author expresses his thanks for the warm hospitality and facilities provided by Prof. Constantine Tsinakis and the Department of Mathematics of VU. He is greatly indebted to Semnan University for its financial support during the sabbatical.

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