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Rank properties in finite inverse semigroups

Published online by Cambridge University Press:  20 January 2009

Maria Isabel  and
Marques Ribeiro
Maria Isabel
Affiliation:
Departamento de Matemática, Universidade dos Açores, Rua da Mãe de Deus, 9500 Ponta Delgada (Açores), Portugal ([email protected])
Marques Ribeiro
Affiliation:
Departamento de Matemática, Universidade dos Açores, Rua da Mãe de Deus, 9500 Ponta Delgada (Açores), Portugal ([email protected])
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Abstract

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Two possible concepts of rank in inverse semigroup theory, the intermediate I-rank and the upper I-rank, are investigated for the finite aperiodic Brandt semigroup. The so-called large I-rank is found for an arbitrary finite Brandt semigroup, and the result is used to obtain the large rank of the inverse semigroup of all proper subpermutations of a finite set.

Keywords

inverse semigroupBrandt semigrouprankintermediate I-rankupper I-ranklarge I-rank
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 43 , Issue 3 , October 2000 , pp. 559 - 568
Copyright
Copyright © Edinburgh Mathematical Society 2000

References

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