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The Structure of 0-E-unitary inverse semigroups I: the monoid case

Published online by Cambridge University Press:  20 January 2009

Mark V. Lawson
Mark V. Lawson
Affiliation:
Ysgol Fathemateg, Prifysgol Cymru, Bangor, Stryd Y Deon Bangor Gwynedd LL57 1UT Wales
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This is the first of three papers in which we generalise the classical McAlister structure theory for E-unitary inverse semigroups to those 0-E-unitary inverse semigroups which admit a 0-restricted, idempotent pure prehomomorphism to a primitive inverse semigroup. In this paper, we concentrate on finding necessary and sufficient conditions for the existence of such prehomomorphisms in the case of 0-E-unitary inverse monoids. A class of inverse monoids which satisfy our conditions automatically are those which are unambiguous except at zero, such as the polycyclic monoids.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 42 , Issue 3 , October 1999 , pp. 497 - 520
Copyright
Copyright © Edinburgh Mathematical Society 1999

References

REFERENCES

1.Birget, J.-C., Iteration of expansions – unambiguous semigroups, J. Pure Appl. Algebra 34 (1984), 1–55.CrossRefGoogle Scholar
2.Birget, J.-C., Arbitrary vs. regular semigroups, J. Pure Appl. Algebra 34 (1984), 57–115.CrossRefGoogle Scholar
3.Bulman-Fleming, S., Fountain, J. and Gould, V., Strongly E*-unitary inverse semigroups, preprint University of York, England, 07 1997.Google Scholar
4.Clifford, A. H., A class of d-simple semigroups, Amer. J. Math. 15 (1953), 541–556.Google Scholar
5.Clifford, A. H. and Preston, G., The algebraic theory of semigroups, Volume 2 (Mathematical Surveys of the American Mathematical Society, no. 7, 1967, Providence, R.I.).Google Scholar
6.Cohn, P., Universal algebra (D. Reidel, 1981).CrossRefGoogle Scholar
7.Gomes, G. M. S. and Howie, J. M., A P-theorem for inverse semigroups with zero, Portugal. Math. 53 (1996), 257–278.Google Scholar
8.Higgins, Ph., Notes on categories and groupoids (Van Nostrand Reinhold Company, London, 1971).Google Scholar
9.von Karger, B., Embedding sequential calculus in relational calculus, preprint 03 1994.Google Scholar
10.Kellendonk, J., Non-commutative geometry of tilings and gap labelling, Rev. Math. Phys. 7(1995), 1133–1180.CrossRefGoogle Scholar
11.Kellendonk, J., The local structure of tilings and their integer group of coinvariants, Comm. Math. Phys. 187 (1997), 115–157.CrossRefGoogle Scholar
12.Kellendonk, J., Topological equivalence of tilings, J. Math. Phys. 38 (1997), 1823–1842.CrossRefGoogle Scholar
13.Lawson, M. V., The geometric theory of inverse semigroups III, unpublished preprint, University of Wales, Bangor, 1991.Google Scholar
14.Lawson, M. V., The geometric theory of inverse semigroups I: E-unitary inverse semigroups, J. Pure Appl. Algebra 67 (2) (1990), 151–177.CrossRefGoogle Scholar
15.Lawson, M. V., The geometric theory of inverse semigroups II: E-unitary covers of inverse semigroups, J. Pure Appl. Algebra 83 (1992), 121–139.CrossRefGoogle Scholar
16.Lawson, M. V., A class of actions of inverse semigroups, J. Algebra 179 (1996), 570–598.CrossRefGoogle Scholar
17.Lawson, M. V., Constructing inverse semigroups from category actions, J. Pure Appl Algebra, to appear.Google Scholar
18.Lawson, M. V., The structure of 0-E-unitary inverse semigroups II: the general case, in preparation.Google Scholar
19.Lawson, M. V., The structure of 0-E-unitary inverse semigroups III: 0-restricted idempotent pure prehomomorphisms, in preparation.Google Scholar
20.Leech, J., Constructing inverse monoids from small categories, Semigroup Forum 36 (1987), 89–116.CrossRefGoogle Scholar
21.MacLane, S., Categories for the working mathematician (Springer-Verlag, 1971).Google Scholar
22.Margolis, S. W. and Pin, J. E., Inverse semigroups and extensions of groups by semilattices, J. Algebra 110 (1987), 277–297.CrossRefGoogle Scholar
23.McAlister, D. B., 0-bisimple inverse semigroups, Proc. London Math Soc. (3) 28 (1974), 193–221.CrossRefGoogle Scholar
24.McAlister, D. B., ∧-prehomomorphisms on inverse semigroups, Pacific J. Math. 67 (1976), 215–231.CrossRefGoogle Scholar
25.McAlister, D. B., Regular semigroups, fundamental semigroups and groups, J. Austral. Math. Soc. (Ser. A) 29 (1980), 475–503.CrossRefGoogle Scholar
26.Meakin, J. and Sapir, M., Congruences on free monoids and submonoids of polycyclic monoids, J. Austral. Math. Soc. (Ser. A) 54 (1993), 236–253.CrossRefGoogle Scholar
27.Munn, W. D., Brandt congruences on inverse semigroups, Proc. London Math. Soc. (3) 14 (1964), 154–164.CrossRefGoogle Scholar
28.Nivat, M. and Perrot, J.-F., Une généralisation du monoide bicyclique, C. R. Acad. Sci. Paris A 271 (1970), 824–827.Google Scholar
29.Petrich, M., Inverse semigroups (John Wiley, 1984).Google Scholar
30.Reilly, N. R., Bisimple inverse semigroups, Trans. Amer. Math. Soc. 132 (1968), 101–114.Google Scholar
31.Szendrei, M. B., A generalisation of McAlister's P-theorem for E-unitary regular semigroups, Acta Sci. Math. (Szeged) 51 (1987), 229–249.Google Scholar
32.Weibel, C. A., An introduction to homological algebra (Cambridge University Press, 1995).Google Scholar