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On strongly flat and condition (P) S-posets

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Abstract

In this paper, we first present some homological classifications of pomonoids by using condition (P) and strongly flat properties. Unlike the case for acts, condition (P) and strongly flat coincide for cyclic right S-posets when all weakly right reversible convex subpomonoids of a pomonoid S are left collapsible. Thereby we characterize pomonoids over which strong flatness and condition (P) imply some other flatness properties. Furthermore, we characterize a pomonoid over which every right S-poset has a strongly flat (condition (P)) cover.

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References

  1. Bulman-Fleming, S., Laan, V.: Lazard’s theorem for S-posets. Math. Nachr. 278(15), 1743–1755 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bulman-Fleming, S., Normak, P.: Flatness properties of monocyclic acts. Monatsh. Math. 122, 307–323 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  3. Bulman-Fleming, S., Gutermuth, D., Glimour, A., Kilp, M.: Flatness properties of S-posets. Commun. Algebra 34, 1291–1317 (2006)

    Article  MATH  Google Scholar 

  4. Fountain, J.: Perfect semigroups. Proc. Edinburgh Math. Soc. 20(3), 87–93 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  5. Gould, V., Shaheen, L.: Perfection for pomonoids. Semigroup Forum 81, 102–127 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  6. Husheng, Q., Zhongkui, L.: On the homological classification of pomonoids by their Rees factor S-posets. Semigroup Forum 79, 385–399 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  7. Isbell, J.: Perfect monoids. Semigroup Forum 2, 95–118 (1971)

    Article  MathSciNet  MATH  Google Scholar 

  8. Khosravi, R., Ershad, M., Sedaghatjoo, M.: Strongly flat and condition (P) covers of acts over monoids. Commun. Algebra. doi:10.1080/00927870903390660

  9. Kilp, M., Knauer, U., Mikhalev, A.: Monoids, Acts and Categories. W. de Gruyter, Berlin (2000)

    MATH  Google Scholar 

  10. Kilp, M.: On monoids all strongly flat cyclic right acts over which are projective. Semigroup Forum 52, 241–245 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  11. Kilp, M.: Perfect monoids revisited. Semigroup Forum 53, 225–229 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  12. Mahmoudi, M., Renshaw, J.: On covers of cyclic acts over monoids. Semigroup Forum 77, 325–338 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  13. Shi, X.: Strongly flat and po-flat S-posets. Communications in Algebra 33, 4515–4531 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  14. Shi, X.: On flatness properties of cyclic S-posets. Semigroup Forum 77, 248–266 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  15. Shi, X., Lui, Z., Wang, F., Bulman-Fleming, S.: Indecomposable, projective, and flat S-posets. Communications in Algebra 33, 235–251 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  16. Tajnia, S.: Projective covers in POS-S. Tarbiat Moallem University, 20th Seminar on Algebra, 210–212, 2–3 Ordibhest (1388), 22–23 April 2009

  17. Xie, X., Shi, X.: Order-congruences on S-posets. Commun. Korean Math. Soc. 20(1), 1–14 (2005)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, College of Sciences, Shiraz University, Shiraz, Iran

    M. Ershad & R. Khosravi

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  1. M. Ershad
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  2. R. Khosravi
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Correspondence to M. Ershad.

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Communicated by Steve Pride.

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Ershad, M., Khosravi, R. On strongly flat and condition (P) S-posets. Semigroup Forum 82, 530–541 (2011). https://doi.org/10.1007/s00233-010-9283-5

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  • DOI: https://doi.org/10.1007/s00233-010-9283-5

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