Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-23T19:12:22.652Z Has data issue: false hasContentIssue false
  • English
  • Français

Flatness properties of acts over commutative, cancellative monoids

Part of: Semigroups

Published online by Cambridge University Press:  26 February 2010

Sydney Bulman-Fleming
Sydney Bulman-Fleming
Affiliation:
Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario N2L 3C5, Canada. e-mail: [email protected]
Get access

Abstract

This note presents a classification of commutative, cancellative monoids S by flatness properties of their associated S-acts.

MSC classification

Secondary: 20M10: General structure theory
Type
Research Article
Information
Mathematika , Volume 46 , Issue 1 , June 1999 , pp. 93 - 102
Copyright
Copyright © University College London 1999

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Bulman-Fleming, S. The classification of monoids by flatness properties of acts. Proc 1997 St. Andrews Conf. on Semigroups and their Applications, World Scientific. (1998), 18–38.Google Scholar
2.Bulman-Fleming, S.Flat and strongly flat S-systems. Communications in Algebra, 20 (9) (1992), 2553–2567.CrossRefGoogle Scholar
3.Bulman-Fleming, S. and McDowell, K.Monoids over which all weakly flat acts are flat. Proc. Edinburgh Math. Soc., 33 (1990), 287–298.Google Scholar
4.Bulman-Fleming, S.. and Normak, P.Flatness properties of monocyclic acts. Mh. Math., 122 (1996), 307–323.CrossRefGoogle Scholar
5.Kilp, M..On monoids over which all strongly flat cyclic right acts are projective. Semigroup Forum, 52 (1996), 241–245.Google Scholar
6.Kilp, M..Characterization of monoids by properties of their left Rees factors, Tartu Riikl. Ul. Toimetised, 640 (1983), 29–37.Google Scholar
7.Kilp, M.. and Knauer, U.On free, projective, and strongly flat acts. Arch. Math., 47 (1986), 17–23.CrossRefGoogle Scholar
8.Knauer, U.. and Petrich, M.Characterization of monoids by torsion-free, flat, projective and free acts. Arch. Math., 36 (1981), 289–294.Google Scholar
9.Zhongkui, LiuCharacterization of monoids by condition (P) of cyclic left acts. Semigroup Forum, 49 (1994), 31–49.CrossRefGoogle Scholar
10.Normak, P.On equalizer flat and pullback flat acts. Semigroup Forum, 36 (1987), 293–313.Google Scholar