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ON FLATNESS COVERS OF CYCLIC ACTS OVER MONOIDS

Published online by Cambridge University Press:  09 December 2011

HUSHENG QIAO  and
LIMIN WANG
HUSHENG QIAO
Affiliation:
Department of Mathematics, Northwest Normal University Lanzhou 730070, Gansu, China e-mail: [email protected]
LIMIN WANG
Affiliation:
Department of Mathematics, Northwest Normal University Lanzhou 730070, Gansu, China e-mail: [email protected]
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Abstract

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The covers of cyclic acts over monoids were investigated by Mahmoudi and Renshaw (M. Mahmoudi and J. Renshaw, On covers of cyclic acts over monoids, Semigroup Forum77 (2008), 325–338) and the authors posed some open problems. In the present paper, we give answers to their problems 1 and 5, and we also give a sufficient and necessary condition that a cyclic act has a weakly pullback flat cover.

Keywords

20M30
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 54 , Issue 1 , January 2012 , pp. 163 - 167
Copyright
Copyright © Glasgow Mathematical Journal Trust 2011

References

REFERENCES

1.Amini, A., Ershad, M. and Sharif, H., Rings over which flat covers of finitely generated modules are projective, Comm. Algebra 36 (8) (2008), 2862–2871.CrossRefGoogle Scholar
2.Stenström, B., Flatness and localization over monoids, Math. Nachr. 48 (1971), 315–334.CrossRefGoogle Scholar
3.Enochs, E. E., Jenda, O. M. G. and Lopez-Ramos, J. A., The existence of Gorenstein flat covers, Math. Scand. 94 (2004), 46–62.CrossRefGoogle Scholar
4.Enochs, E. E. and Oyonarte, L., Covers, envelopes and cotorsion theories (Nova Science, New York, 2002).Google Scholar
5.Fountain, J., Perfect semigroups, Proc. Edinb. Math. Soc. 20 (2) (1976), 87–93.CrossRefGoogle Scholar
6.Howie, J. M., Fundamentals of semigroup theory. London Mathematical Society Monograph (London Mathematical Society, London, 1995)Google Scholar
7.Isbell, J., Perfect monoids, Semigroup Forum 2 (1971), 95–118.Google Scholar
8.Kilp, M., Perfect monoids revisited, Semigroup Forum 53 (1996), 225–229.Google Scholar
9.Kilp, M. and Laan, V., On flatness properties of cyclic acts, Comm. Algebra 28 (6) (2000), 2919–2926.Google Scholar
10.Kilp, M., On monoids over which all strongly flat cyclic right acts are projective, Semigroup Forum 52 (1996), 241–245.CrossRefGoogle Scholar
11.Kilp, M., Knauer, U., Mikhalev, A. V., Monoids, acts and categories, in De Gruyter expositions in mathematics, Vol. 29, (de Gruyter, Berlin, 2000).Google Scholar
12.Mao, L. and Ding, N., Envelopes and covers by modules of finite FP-injective and flat dimensions, Comm. Algebra 35 (3) (2007), 833–849.CrossRefGoogle Scholar
13.Mahmoudi, M. and Renshaw, J., On covers of cyclic acts over monoids. Semigroup Forum 77 (2008), 325–338.CrossRefGoogle Scholar
14.Laan, V., On a generalization of strong flatness. Acta Comment, Univ. Tartu. Math. 2 (1998), 55–60.Google Scholar
15.Xu, J., Flat covers of modules, in Lecture Notes in Mathematics, Vol. 1634 (Springer, Berlin, 1996).Google Scholar