Regular subsemigroups of the semigroups of transformations preserving a fence. (Q2806079)
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scientific article; zbMATH DE number 6580710
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Regular subsemigroups of the semigroups of transformations preserving a fence. |
scientific article; zbMATH DE number 6580710 |
Statements
13 May 2016
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semigroups of transformations
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coregular semigroups
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regular elements
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regular subsemigroups
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relation preserving transformations
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fences
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Regular subsemigroups of the semigroups of transformations preserving a fence. (English)
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A fence is a partially ordered set whose Hasse diagram has a zig-zag form with maximal chains of length two. The paper under review studies two subsemigroups of the full transformation semigroup which preserve a fixed fence. The first one is the subsemigroup of all order decreasing transformations and the second one is the subsemigroup of all order preserving transformations. It is shown that the first one is coregular. It is also shown that the second one is regular if and only if the underlying set has at most four elements. Regularity of elements in the second semigroup is discussed.
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