Remarks on isomorphisms of transformation semigroups restricted by an equivalence relation
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Let $T(X)$ be the full transformation semigroup on a set $X$ and $\sigma$ be an equivalence relation on $X$. Denote \[ E(X, \sigma) = \{\alpha \in T(X) : \forall x, y \in X, (x, y) \in \sigma \mbox{ implies } x\alpha = y\alpha \}. \] Then $E(X, \sigma)$ is a subsemigroup of $T(X)$. In this paper, we characterize two semigroups of type $E(X, \sigma)$ when they are isomorphic.
Abstract
Let $T(X)$ be the full transformation semigroup on a set $X$ and $\sigma$ be an equivalence relation on $X$. Denote \[ E(X, \sigma) = \{\alpha \in T(X) : \forall x, y \in X, (x, y) \in \sigma \mbox{ implies } x\alpha = y\alpha \}. \] Then $E(X, \sigma)$ is a subsemigroup of $T(X)$. In this paper, we characterize two semigroups of type $E(X, \sigma)$ when they are isomorphic.
참고문헌 (7)
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