Upper-modular elements of the lattice of semigroup varieties (Q1001463)
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scientific article; zbMATH DE number 5508756
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Upper-modular elements of the lattice of semigroup varieties |
scientific article; zbMATH DE number 5508756 |
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Upper-modular elements of the lattice of semigroup varieties (English)
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17 February 2009
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The author proves that if a proper semigroup variety \(\mathbf V\) is an upper-modular element in the lattice of all semigroup varieties, then \(\mathbf V\) is periodic and the largest nil-subvariety of \(\mathbf V\) satisfies the identities \(xy=yx\), \(x^2y=xy^2\). This allows the author to classify all commutative varieties that are upper-modular elements in the lattice of all semigroup varieties.
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semigroup variety
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lattice of semigroup varieties
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upper-modular element
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periodic variety
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nilvariety
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variety of finite index
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