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- W2048002508 abstract "Abstract Let ${ mathcal{T} }_{X} $ be the full transformation semigroup on a set $X$ and $E$ be a nontrivial equivalence relation on $X$ . Denote $$begin{eqnarray*}{T}_{exists } (X)= { fin { mathcal{T} }_{X} : forall x, yin X, (f(x), f(y))in ERightarrow (x, y)in E} ,end{eqnarray*}$$ so that ${T}_{exists } (X)$ is a subsemigroup of ${ mathcal{T} }_{X} $ . In this paper, we endow ${T}_{exists } (X)$ with the natural partial order and investigate when two elements are related, then find elements which are compatible. Also, we characterise the minimal and maximal elements." @default.
- W2048002508 created "2016-06-24" @default.
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- W2048002508 date "2013-01-25" @default.
- W2048002508 modified "2023-10-16" @default.
- W2048002508 title "THE NATURAL PARTIAL ORDER ON THE SEMIGROUP OF ALL TRANSFORMATIONS OF A SET THAT REFLECT AN EQUIVALENCE RELATION" @default.
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- W2048002508 doi "https://doi.org/10.1017/s0004972712001013" @default.
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