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Monoids over which all weakly flat acts are flat

Published online by Cambridge University Press:  20 January 2009

Sydney Bulman-Fleming  and
Kenneth McDowell
Sydney Bulman-Fleming
Affiliation:
Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario, Canada, N2L 3C5
Kenneth McDowell
Affiliation:
Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario, Canada, N2L 3C5
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Abstract

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If R is a ring with identity and M is a left R-module then it is well known that the following statements are equivalent:

(1) M is flat.

(2) The functor −⊗M preserves embeddings of right ideals into R.

This paper investigates situations in which the analogous statements are equivalent in the context of S-sets over a monoid S.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 33 , Issue 2 , June 1990 , pp. 287 - 298
Copyright
Copyright © Edinburgh Mathematical Society 1990

References

REFERENCES

1.Bourbaki, N., Commutative Algebra (Addison-Wesley, Reading, Mass., 1972).Google Scholar
2.Bulman-Fleming, S. and McDowell, K., Absolutely flat semigroups, Pacific J. Math. 107 (1983), 319–333.CrossRefGoogle Scholar
3.Bulman-Fleming, S. and McDowell, K., Left absolutely flat generalized inverse semigroups, Proc. Amer. Math. Soc. 94 (1985), 553–561.CrossRefGoogle Scholar
4.Bulman-Fleming, S. and McDowell, K., A characterization of left cancellative monoids by flatness properties, Semigroup Forum 40 (1990), 109–112.CrossRefGoogle Scholar
5.Bulman-Fleming, S. and McDowell, K., On V. Fleischer's characterization of absolutely flat monoids, Algebra Universalis 25 (1988), 394–399.CrossRefGoogle Scholar
6.Clifford, A. H. and Preston, G. B., The Algebraic Theory of Semigroups; vol. II (Mathematical Surveys of the American Math. Soc. 7, Providence, R.I., 1967).Google Scholar
7.Howie, J. M., An Introduction to Semigroup Theory (Academic Press, London, 1976).Google Scholar
8.Fleischer, V., Completely flat monoids, Učh. Zap. Tartu Un-ta 610 (1982), 38–52 (Russian). (MR85:20178). (English translation: Amer. Math. Soc. Transl. (2) 142 (1989), 19–31.)Google Scholar
9.Fountain, J., Right PP monoids with central idempotents, Semigroup Forum 13 (1977), 229–237.CrossRefGoogle Scholar
10.Kilp, M., On completely flat monoids, Tartu Riikl. Ūl. Toimetised 700 (1985), 32–37.Google Scholar
11.Kilp, M., Strong flatness of flat cyclic left acts, Tartu Riikl. Ūl. Toimetised 700 (1985), 38–41.Google Scholar
12.Kilp, M., Commutative monoids all of whose principal ideals are projective, Semigroup Forum 6 (1973), 334–339.CrossRefGoogle Scholar
13.Knauer, U. and Petrich, M., Characterization of monoids by torsion-free, flat, projective and free acts, Arch. Math. 36 (1981), 289–294.CrossRefGoogle Scholar
14.Normak, P., On equalizer-flat and pullback-flat acts, Semigroup Forum 36 (1987), 293–313.CrossRefGoogle Scholar
15.Yamada, M., Regular semigroups whose idempotents satisfy permutation identities, Pacific J. Math. 21 (1967), 371–392.CrossRefGoogle Scholar