A note on abundance of certain semigroups of transformations with restricted range |
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| Authors: | Lei Sun |
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| Affiliation: | 1. School of Mathematics and Information Science, Henan Polytechnic University, Henan, Jiaozuo, 454003, P.R. China
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| Abstract: | Given a set X and a nonempty Y?X, we denote by T(X,Y) the subsemigroup of the full transformation semigroup on X consisting of all transformations whose range is contained in Y. We show that the semigroup T(X,Y) is right abundant but not left abundant whenever Y is a proper non-singleton subset of X. |
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