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upper i-rank

Proceedings of the Edinburgh Mathematical Society (1)

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Rank properties in finite inverse semigroups
Maria Isabel, Marques Ribeiro
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 43 / Issue 3 / October 2000

Published online by Cambridge University Press:

20 January 2009, pp. 559-568
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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.