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Pullback-Flat Acts are Strongly Flat

Published online by Cambridge University Press:  20 November 2018

Sydney Bulman-Fleming
Sydney Bulman-Fleming*
Affiliation:
Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario N2L 3C5
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Abstract

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Let 5 be a monoid. A right S-system A is called strongly flat if the functor A ⊗ — (from the category of left S-systems into the category of sets) preserves pullbacksand equalizers. (This concept arises in B. Stenström, Math. Nachr. 48(1971), 315-334 under the name weak flatness). The main result of the present paper is a proof that for A to be strongly flat it is in fact sufficient that A ⊗ — preserve only pullbacks. The approach taken is to develop an "interpolation" condition for pullback-preservation, and then to show its equivalence to Stenström's conditions for strong flatness.

Keywords

20M1020M50

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 34 , Issue 4 , 01 December 1991 , pp. 456 - 461
Copyright
Copyright © Canadian Mathematical Society 1991

References

1. S. Bulman-Fleming and McDowell, K., Absolutely flat semigroups, Pacific J. Math. 107 (1983), 319–333.Google Scholar
2. S. Bulman-Fleming and McDowell, K., Monoids over which all weakly flat acts are flat, Proc. Edinburgh Math. Soc. 33 (1990), 287–298.Google Scholar
3. Normak, P., On equalizer-flat and pullback-flat acts, Semigroup Forum 36 (1987), 293–313.Google Scholar
4. Renshaw, J., Flatness and amalgamation in monoids, J. London Math. Soc. (2)33 (1986), 73–88.Google Scholar
5. B. Stenstrôm, Flatness and localization over monoids, Math. Nachr. 48 (1971), 315–334.Google Scholar