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Valuations and Prufer Rings

Published online by Cambridge University Press:  20 November 2018

Malcolm Griffin
Malcolm Griffin*
Affiliation:
Queen's University, Kingston, Ontario
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The word ring is used to mean commutative ring. Just as valuations on fields are used to study domains, so valuations on rings can be used to study rings; these rings need not have units [12]. We introduce slightly weaker conditions than having identity in order to get a more general theory. A Prufer ring A is one in which every finitely generated regular ideal is invertible. If we replace invertibility in the total quotient ring K, by invertibility in a ring R where A ⊆ R ⊆ K we get an R-Prufer ring. These rings do occur, for example the Witt ring of a non-Pythagorean field or a ring of bounded continuous functions.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 2 , April 1974 , pp. 412 - 429
Copyright
Copyright © Canadian Mathematical Society 1974

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