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On the nilpotent ranks of certain semigroups of transformations

Published online by Cambridge University Press:  18 May 2009

G. U. Garba
G. U. Garba
Affiliation:
Department of Mathematical and Computational Sciences, University of St Andrews, Scotland
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Let Pn be the semigroup of all partial transformations on the set Xn = {1,…, n}. As usual, we shall say that an element α in Pn is of type (k, r) or belongs to the set [k, r] if |dom α|=k and |lim α|. The completion α* of an element α ∈ [n − 1, n − 1] is an element in [n, n] defined by

where {i} = Xn∖dom α and {j} = Xn∖im α.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 36 , Issue 1 , January 1994 , pp. 1 - 9
Copyright
Copyright © Glasgow Mathematical Journal Trust 1994

References

REFERENCES

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