Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-19T10:33:09.575Z Has data issue: false hasContentIssue false
  • English
  • Français

Completely 0-simple semigroups of quotients III

Published online by Cambridge University Press:  24 October 2008

John Fountain  and
Mario Petrich
John Fountain
Affiliation:
Department of Mathematics, University of York, York Y01 5DD
Mario Petrich
Affiliation:
Department of Mathematics, University of York, York Y01 5DD
Get access Rights & Permissions [Opens in a new window]

Extract

In a recent paper [6] the authors introduced the concept of a completely 0-simple semigroup of quotients. This definition has since been extended to the class of all semigroups giving a definition of semigroup of quotients which may be regarded as an analogue of the classical ring of quotients. When Q is a sernigroup of quotients of a semigroup S, we also say that S is an order in Q.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 105 , Issue 2 , March 1989 , pp. 263 - 275
Copyright
Copyright © Cambridge Philosophical Society 1989

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

REFERENCES

[1]Clifford, A. H.. The free completely regular semigroup on a set. J. Algebra 59 (1979), 434–451.CrossRefGoogle Scholar
[2]Clifford, A. H. and Preston, G. B.. The Algebraic Theory of Semigroups, vol. I. Math. Surveys no. 7 (American Mathematical Society, 1961).Google Scholar
[3]Fountain, J. B.. Abundant semigroups. Proc. London Math. Soc. (2) 44 (1982), 103–129.CrossRefGoogle Scholar
[4]Fountain, J. B. and Gould, V. A. R.. Completely 0-simple semigroups of quotients II. In Contributions to General Algebra 3 (Verlag Hölder–Pichler–Temperly, 1985), pp. 115–124.Google Scholar
[5]Fountain, J. B. and Petrich, M.. Brandt semigroups of quotients. Math. Proc. Camb. Philos. Soc. 98 (1985), 413–426.CrossRefGoogle Scholar
[6]Fountain, J. B. and Petrich, M.. Completely 0-simple semigroups of quotients. J. Algebra 101 (1986), 365–402.CrossRefGoogle Scholar
[7]Gould, V.. Orders in semigroups. In Contributions to General Algebra 5 (Verlag Hölder–Pichler–Temperly, 1987), pp. 163–169.Google Scholar
[8]Lallement, G. and Petrich, M.. Decompositions I-matricielles d'un demi-groupe. J. Math. Pures Appl. (9) 45 (1966), 67–117.Google Scholar
[9]Lyndon, R. C. and Schupp, P. E.. Combinatorial Group Theory (Springer-Verlag, 1977).Google Scholar
[10]McAlister, D. B.. One-to-one partial right translations of a right cancellative semigroup. J. Algebra 43 (1976), 231–251.CrossRefGoogle Scholar
[11]Pastijn, F.. A representation of a semigroup by a semigroup of matrices over a group with zero. Semigroup Forum 10 (1975), 238–249.CrossRefGoogle Scholar
[12]Petrich, M.. Lectures in Semigroups (Wiley, 1977).CrossRefGoogle Scholar
[13]Petrich, M.. Normal bands of commutative cancellative semigroups. Duke Math. J. 40 (1973), 17–32.CrossRefGoogle Scholar
[14]Petrich, M.. Dense extensions of a completely 0-simple semigroup I. J. Reine Angew. Math. 258 (1973), 103–125.Google Scholar
[15]Petrich, M.. Monogenic endomorphisms of a free monoid. (Preprint.)Google Scholar
[16]Rasin, V. V.. Free completely simple semigroups. In Research in Contemporary Algebra, Matem. Zapiski (Sverdlovsk) (1979), pp. 140–151 (Russian).Google Scholar
[17]Streilein, J. J.. An embedding theorem for matrices of commutative cancellative semi-groups. Trans. Amer. Math. Soc. 208 (1975), 127–140.CrossRefGoogle Scholar