Maximal \(n\)-generated subdirect products. (Q2796982)
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scientific article; zbMATH DE number 6561295
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Maximal \(n\)-generated subdirect products. |
scientific article; zbMATH DE number 6561295 |
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30 March 2016
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finite algebras
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arithmetical varieties
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interpolation
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free algebras
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clones
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finitely generated algebras
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subdirect powers
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primal algebras
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primal clusters
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subdirectly irreducible algebras
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0.8661703
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0.8603669
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Maximal \(n\)-generated subdirect products. (English)
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Let \(\mathbf K\) be a finite set of finite algebras of the same similarity type and let \(n\) be a positive integer. Consider an \(n\)-generated algebra \(A\) which is a subdirect product of algebras in \(\mathbf K\). The aim of this paper is to answer the question: what is the largest possible size of \(A\)? Note that for particular \(\mathbf K\) such algebra \(A\) is just a free algebra in a variety.NEWLINENEWLINE First, the author collects and discusses earlier results obtained in this direction by G.~Birkhoff, A.~L.~Foster, A.~F.~Pixley, F.~M.~Sioson and W.~Sierpiński which motivated his study. He gives a common framework for them. The Main Theorem 7.1. extends all these results. There are also examples which explain in details how to apply the Main Theorem.
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