Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-27T02:16:10.771Z Has data issue: false hasContentIssue false
  • English
  • Français

Almost factorisable inverse semigroups

Published online by Cambridge University Press:  18 May 2009

M. V. Lawson
M. V. Lawson
Affiliation:
University College of North Wales, School of Mathematics, Dean Street, Bangor, Gwynedd, LL57 1UT, Cymru/WalesU.K.
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In [3], McAlister introduced a class of semigroups, called covering semigroups, which were shown to play an important role in the theory of E-unitary covers of semigroups. Strangely, this class of semigroups appears to have received little attention subsequently. It is the aim of this paper to rehabilitate them and to study their properties in more detail. As a first step, we have chosen to rename them almost factorisable semigroups, since they can be regarded as the semigroup analogues of factorisable inverse monoids. Before discussing the contents of this paper in more detail we recall some standard terminology.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 36 , Issue 1 , January 1994 , pp. 97 - 111
Copyright
Copyright © Glasgow Mathematical Journal Trust 1994

References

REFERENCES

1.Lawson, M. V., The geometric theory of inverse semigroups II: E-unitary covers of inverse semigroups, J. Pure and Applied Algebra 83 (1992), 121–139.CrossRefGoogle Scholar
2.Lawson, M. V., An equivalence theorem for inverse semigroups, Semigroup Forum 47 (1993), 7–14.CrossRefGoogle Scholar
3.McAlister, D. B., Some covering and embedding theorems for inverse semigroups, J. Australian Math. Soc. 22 (Series A) (1976), 188–211.CrossRefGoogle Scholar
4.McAlister, D. B., E-unitary inverse semigroups over semilattices, Glasgow Math. J. 19 (1978), 1–12.CrossRefGoogle Scholar
5.McAlister, D. B., Some covering theorems for locally inverse semigroups, J. Australian Math. Soc. 39 (Series A) (1985), 63–74.CrossRefGoogle Scholar
6.Nambooripad, K. S. S., The natural partial order on a regular semigroup, Proc. Edinburgh Math. Soc. 23 (1980), 249–260.CrossRefGoogle Scholar
7.Petrich, M., Inverse semigroups (Wiley, 1984).Google Scholar
8.Reilly, N. R. and Munn, W. D., E-unitary congruences on inverse semigroups, Glasgow Math. J. 17 (1976), 57–75.CrossRefGoogle Scholar
9.Rhodes, J. (editor), Monoids and semigroups with applications (World Scientific, 1991).CrossRefGoogle Scholar
10.Schein, B., Completions, translational hulls and ideal extensions of inverse semigroups, Czechoslovak Math. J. 23 (1973), 575–610.CrossRefGoogle Scholar