### Some Transformation Semigroups Admitting Nearing Structure

#### Abstract

Denote by

*T*(*X*) and*P*(*X*) the full transformation semigroup andthe partial transformation semigroup on a nonempty set*X*, respectively. The semigroups*T*(*X*) and*P*(*X*) are known to admit a right nearring structure for any*X*and they admit a left nearring structure only the case that $|*X|*= 1$. We generalize these results to the semigroups*T*(*X, Y*) and*P*(*X, Y*) under composition where*$\emptyset \neg**Y \subset X*,*T*(*X, Y*) = {\alpha \in*T*(*X*)|*ran \alpha**\subset Y }*and*P(**X, Y*) = {\alpha \in*P*(*X*) | ran \alpha*\subset Y }$*. We obtain the analogous results that*T*(*X, Y*) and*P*(*X, Y*) admit a right nearring structure for any*$\emptyset \neg Y \subset X$ and $|**Y |*= 1$ is necessary and sufficient for them to admit a left nearring structure.### Refbacks

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