The cocycle equation on periodic semigroups (Q1291166)
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scientific article; zbMATH DE number 1295518
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The cocycle equation on periodic semigroups |
scientific article; zbMATH DE number 1295518 |
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The cocycle equation on periodic semigroups (English)
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15 September 1999
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The main result offered by the authors is that all solutions, mapping the Cartesian square of an abelian periodic semigroup (one in which every element is of finite order) into a uniquely divisible abelian group, of the functional equation \(F(x,y)+F(xy,z)=F(xy,z)+F(y,z)\) are of the form \(F(x,y)=f(x)+f(y)-f(xy).\)
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cocycle equation
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coboundary
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Cauchy difference
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abelian periodic semigroups
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uniquely divisible abelian groups
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functional equations
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