Green's equivalences on semigroups of transformations preserving order and an equivalence relation. (Q818959)
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scientific article; zbMATH DE number 5014181
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Green's equivalences on semigroups of transformations preserving order and an equivalence relation. |
scientific article; zbMATH DE number 5014181 |
Statements
Green's equivalences on semigroups of transformations preserving order and an equivalence relation. (English)
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22 March 2006
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The subject of this paper is the subsemigroup of all order-preserving mappings of the semigroup of all mappings on the finite chain \(X\) that preserve a given equivalence relation \(E\) on \(X\). In addition it is assumed that \(E\) consists of \(m\) classes of \(n\) consecutive points with \(m,n\geq 2\). The authors determine Green's relations and the regular elements of this semigroup which itself is not regular.
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full transformation semigroups
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order-preserving mappings
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regular elements
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Green relations
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