Varieties having Boolean factor congruences (Q1813837)
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scientific article; zbMATH DE number 5239
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Varieties having Boolean factor congruences |
scientific article; zbMATH DE number 5239 |
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Varieties having Boolean factor congruences (English)
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25 June 1992
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In the paper, the varieties having Boolean factor congruences (BFC) or, equivalently, the strict refinement property are studied aiming at finding a Mal'cev condition for BFC. The main results are as follows: 1. A sufficient condition for BFC, denoted by (*), is given in terms of a first-order definable 4-ary relation. 2. Every variety known to have BFC (e.g., those having the Fraser-Horn-Hu property) satisfies (*). 3. Every centerless variety has BFC, but not vice versa. 4. For congruence-modular varieties and Jónsson-Tarski varieties, (*) is equivalent to BFC and also to the absence of nontrivial abelian algebras.
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Boolean factor congruences
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strict refinement property
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centerless variety
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congruence-modular varieties
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Jónsson-Tarski varieties
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abelian algebras
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