On the classes of algebras reciprocally closed under direct products (Q2729637)
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scientific article; zbMATH DE number 1623101
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the classes of algebras reciprocally closed under direct products |
scientific article; zbMATH DE number 1623101 |
Statements
6 December 2001
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group isotopes
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\(n\)-ary quasigroups
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reciprocally closed classes of algebras
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direct products
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On the classes of algebras reciprocally closed under direct products (English)
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A class \(K\) of algebras is called reciprocally closed under direct products or RC [see \textit{A. Horn}, J. Symb. Logic 16, 14-21 (1951; Zbl 0043.24801)] if two algebras belong to \(K\) iff their direct product belongs to \(K\). It is proved that the class of all group isotopes and the class of all \(i\)-linear \(n\)-ary group isotopes, where \(i\) and \(n\) are fixed, are RC.
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