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Extensions of a semilattice by an inverse semigroup

Published online by Cambridge University Press:  17 April 2009

D.G. Green
D.G. Green
Affiliation:
Department of Mathematics, Monash university, Clayton, Victoria.
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Abstract

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The structure of inverse semigroup extensions of one inverse semigroup R by any other is analyzed in the case where R is a semilattice. Both a representation and method of construction are given. A brief preliminary examination is made of a certain class of congruences, on inverse semigroups, which are intimately related to such extensions.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 9 , Issue 1 , August 1973 , pp. 21 - 31
Copyright
Copyright © Australian Mathematical Society 1973

References

[1]Clifford, A.H. and Preston, G.B., The algebraic theory of semigroups, Volume I (Math. Surveys 7 (I), Amer. Math. Soc., Providence, Rhode Island, 1961).Google Scholar
[2]Clifford, A.H. and Preston, G.B., The algebraic theory of semigroups, Volume II (Math. Surveys 7 (II), Amer. Math. Soc., Providence, Rhode Island, 1967).Google Scholar
[3]Coudron, A., “Sur les extensions de demi-groupes réciproques”, Bull. Soc. Roy. Sci. Liège 37 (1968), 409–419.Google Scholar
[4]D'Alarcao, H., “Idempotent-separating extensions of inverse semigroups”, J. Austral. Math. Soc. 9 (1969), 211–217.CrossRefGoogle Scholar
[5]McFadden, R. and O'Carroll, L., “F-inverse semigroups”, Proc. London Math. Soc. (3) 22 (1971), 652–666.CrossRefGoogle Scholar
[6]Preston, G.B., “Free inverse semigroups”, J. Austral. Math. Soc. (to appear).Google Scholar
[7]Scheiblich, H.E., “Free inverse semigroups”, Semigroup Forum 4 (1972), 351–359.CrossRefGoogle Scholar