Complete semigroups of binary relations determined by three-element \(X\)-chains. (Q1416170)
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scientific article; zbMATH DE number 2016959
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Complete semigroups of binary relations determined by three-element \(X\)-chains. |
scientific article; zbMATH DE number 2016959 |
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Complete semigroups of binary relations determined by three-element \(X\)-chains. (English)
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14 December 2003
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This paper considers the subgroups of the semigroup of binary relations \(B_X\) consisting of binary relations \(R\) whose sections \(S_x=\{y\mid(x,y)\in R\}\) are always equal to some \(Z_i\), for a 3 element chain \(Z_1\subset Z_2\subset Z_3\). It determines idempotents, regular elements, maximal semigroups consisting of idempotents, and irreducible generating sets, and computes the cardinalities of some of these for finite sets.
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semigroups of binary relations
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idempotent binary relations
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regular binary relations
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idempotents
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generating sets
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