On the weak Grothendieck group of a Bézout ring (Q2816784)
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scientific article; zbMATH DE number 6619350
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the weak Grothendieck group of a Bézout ring |
scientific article; zbMATH DE number 6619350 |
Statements
25 August 2016
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Witt vectors
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On the weak Grothendieck group of a Bézout ring (English)
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A commutative ring \(R\) is called a Bézout ring if every finitely generated ideal is principal. The weak Grothendieck group \(K'_0(R)\) is defined using cyclic \(R\)-modules rather than finitely generated projective modules used for definition of the Grothendieck group \(K_0(R)\). Theorem 6 connect \(K'_0(R)\) with Witt vectors. Theorem 8 asserts that \(K'_0(R) = K_0(R)\) for commutative von Neumann regular \(R\).
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