Equational theories for classes of finite semigroups (Q2714065)
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scientific article; zbMATH DE number 1603326
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Equational theories for classes of finite semigroups |
scientific article; zbMATH DE number 1603326 |
Statements
10 June 2001
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equational theory
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finite semigroup
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0.95177305
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0.93347704
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0.9299431
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0.9267633
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0.90873367
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0.90862024
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Equational theories for classes of finite semigroups (English)
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Theorem 1. There exists an infinite sequence of finitely based varieties of semigroups \(A_1\subset B_1\subset A_2\subset B_2\subset\cdots\) such that for all \(i\) the equational theories of \(A_i\) and of the classes \(A_i\cap F\) of all finite semigroups in \(A_i\) are undecidable while the equational theories of \(B_i\) and of the class \(B_i\cap F\) of all finite semigroups in \(B_i\) are decidable.NEWLINENEWLINENEWLINETheorem 2. There exists an infinite sequence of finitely based varieties of semigroups \(A_1\supset B_1\supset A_2\supset B_2\supset\cdots\) such that for all \(i\) the equational theories of \(A_i\) and of the classes \(A_i\cap F\) of all finite semigroups in \(A_i\) are undecidable while the equational theories of \(B_i\) and of the class \(B_i\cap F\) of all finite semigroups in \(B_i\) are decidable.
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