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On the homological classification of pomonoids: Clifford pomonoids

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Abstract

In two recent papers by the author for pomonoids, which as monoids are completely simple semigroups with adjoined identity, or semilattices, conditions under which their Rees factor \(S\)-posets satisfy property \((\mathrm{P}_w)\) were found. In this paper pomonoids, which as monoids are Clifford semigroups whose submonoids of idempotents are semilattices satisfying the minimum condition, all of whose Rees factor \(S\)-posets satisfy property \((\mathrm{P}_w)\) are characterized.

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References

  1. Bulman-Fleming, S.: Flatness properties of \(S\)-posets: an overview. Tartu conference on monoids, acts and categories, with applications to graphs. Math. Proc. Estonian Math. Soc. 3, 28–40 (2008)

    MathSciNet  Google Scholar 

  2. Bulman-Fleming, S., Gutermuth, D., Gilmour, A., Kilp, M.: Flatness properties of \(S\)-posets. Commun. Algebr. 34, 1291–1317 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  3. Golchin, A., Nouri, L.: A correction on the paper “The flatness properties of \(S\)-poset \(A(I)\) and Rees factor \(S\)-posets”. Semigroup Forum doi:10.1007/s00233-014-9608-x

  4. Howie, J.M.: Fundamentals of Semigroup Theory. Oxford Science Publications, Oxford (1995)

    MATH  Google Scholar 

  5. Kilp, M.: On the homological classification of pomonoids by properties of cyclic \(S\)-posets. Semigr. Forum 86, 592–602 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  6. Kilp, M.: On the homological classification of pomonoids: atomic posemilattices. Acta et Commentationes Universitatis Tartuensis de Mathematica 17, 103–111 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  7. Kilp, M., Knauer, U., Mikhalev, A.V.: Monoids, Acts and Categories. Volume 29 of de Gruyter Expositions in Mathematics. Walter de Gruyter, Berlin (2000)

    Book  Google Scholar 

  8. Qiao, H.S., Li, F.: The flatness properties of \(S\)-poset \(A(I)\) and Rees factor \(S\)-posets. Semigr. Forum 77, 306–315 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  9. Shi, X.: Strongly flat and po-flat \(S\)-posets. Commun. Algebr. 33, 4515–4531 (2005)

    Article  MATH  Google Scholar 

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Acknowledgments

The author is grateful to the referee for a number of useful suggestions. Research supported by Estonian Science Foundation Grant No. 8394 and Estonian Institutional Research Project IUT20-57.

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Authors and Affiliations

  1. Institute of Mathematics, University of Tartu, 50090, Tartu, Estonia

    Mati Kilp

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  1. Mati Kilp
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Correspondence to Mati Kilp.

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Communicated by Victoria Gould.

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Kilp, M. On the homological classification of pomonoids: Clifford pomonoids. Semigroup Forum 91, 663–674 (2015). https://doi.org/10.1007/s00233-014-9673-1

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  • DOI: https://doi.org/10.1007/s00233-014-9673-1

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