A combinatorial fact about free algebras (Q790862)
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scientific article; zbMATH DE number 3849302
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A combinatorial fact about free algebras |
scientific article; zbMATH DE number 3849302 |
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A combinatorial fact about free algebras (English)
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1982
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It is shown that every large subset of a free algebra A in a variety contains a large subset X which is homogeneous in a strong sense (i.e. every mapping \(f:X\to X\) extends to an endomorphism \(f^*:A\to A\) in a functorial way - \((fg)^*=f^*g^*\) and \(1_ X=1_ A).\) Consequences of this theorem are derived; e.g.: No free lattice with 0, lattice- ordered group, lattice-ordered ring etc, contains an uncountable set of pairwise disjoint elements.
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first-order language
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large subset
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free algebra
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