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On some open problems of Mahmoudi and Renshaw

Husheng Qiao|Chongqing Wei
대한수학회 (The Korean Mathematical Society)|2014.08|대한수학회보 (Bulletin of the KMS)|제51권 제4호|pp. 1015-1022

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참고문헌

키워드

(P)-coverstrongly flat covercyclic act
주제분류수학

초록

This paper continues the investigation of covers of cyclic acts over monoids. Special attention is paid to (P)-covers and strongly flat covers of cyclic acts. In 2008 Mahmoudi and Renshaw posed some open problems and we gave some examples on them in 2012. In this paper, we obtained some further results on these problems and hence gave some deeper answers to them.

Abstract

This paper continues the investigation of covers of cyclic acts over monoids. Special attention is paid to (P)-covers and strongly flat covers of cyclic acts. In 2008 Mahmoudi and Renshaw posed some open problems and we gave some examples on them in 2012. In this paper, we obtained some further results on these problems and hence gave some deeper answers to them.

참고문헌 (12)

  1. M. Ershad, "On the uniqueness of strongly flat covers of cyclic acts", Turkish J. Math, 35(3), pp.437~442 (2011)
  2. J. Fountain, "Perfect semigroups", Proc. Edinburgh Math. Soc, 20(2), pp.87~93 (1976)
  3. J. M. Howie, "Fundamentals of Semigroup Theory, London Mathematical Society Monographs" (1995), London Math. Soc
  4. J. Isbell, "Perfect monoids", Semigroup Forum, 2(2), pp.95~118 (1971)
  5. R. Khosravi, "Strongly flat and condition (P) covers of acts over monoids", Comm. Algebra, 38(12), pp.4520~4530 (2010)
  6. M. Kilp, "Perfect monoids revisited", Semigroup Forum, 53(2), pp.225~229 (1996)
  7. M. Kilp, "On monoids over which all strongly flat cyclic right acts are projective", Semigroup Forum, 52(2), pp.241~245 (1996)
  8. M. Kilp, "De Gruyter Expositions in Mathematics, vol. 29" (2000), de Gruyter
  9. M. Mahmoudi, "On covers of cyclic acts over monoids", Semigroup Forum, 77(2), pp.325~338 (2008)
  10. H. S. Qiao, "On flatness covers of cyclic acts over monoids", Glasg. Math. J, 54(1), pp.163~167 (2012)
  11. J. Renshaw, "Monoids for which condition (P) acts are projective", Semigroup Forum, 61(1), pp.45~56 (2000)
  12. B. Stenstrom, "Flatness and localization over monoids", Math. Nachr, 48, pp.315~334 (1971)

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