Ideals of free semigroups having cohomological dimension 1 (Q1849722)
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scientific article; zbMATH DE number 1837420
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Ideals of free semigroups having cohomological dimension 1 |
scientific article; zbMATH DE number 1837420 |
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Ideals of free semigroups having cohomological dimension 1 (English)
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1 December 2002
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The article applies the Eilenberg-MacLane definition of cohomology groups and of a cohomological dimension (c.d.) to free semigroups with at least two generators. It is proved that a left ideal of a free semigroup (with at least two generators) has c.d. 1 if and only if it is free. The right hand analogue of this is true only for principal ideals: a principal right ideal of a free semigroup has c.d. 1 if and only if it is free. There is given an example of a right ideal with two generators of a free semigroup with two generators which is not free and has c.d. 1.
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free semigroups
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left ideals
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cohomological dimension
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cohomology groups
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principal right ideals
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