ASSOCIATIONS AND VALUATIONS
作者:
Hans-Heinrich Brungs,
Günter Törner,
期刊:
Quaestiones Mathematicae
(Taylor Available online 1999)
卷期:
Volume 22,
issue 3
页码: 353-363
ISSN:1607-3606
年代: 1999
DOI:10.1080/16073606.1999.9632087
出版商: Taylor & Francis Group
关键词: Primary: 16W60, 16L30;Secondary: 06F05;Valuation ring;right chain ring;right cone;right holoid;right ordered group;associated cones
数据来源: Taylor
摘要:
Right cones are semigroups for which the lattice of right ideals is a chain and a left cancellation law holds; valuation rings, the cones of ordered groups, and initial segments of ordinal numbers are examples. Two such cones are associated if they have isoniorphic lattices of right ideals so that ideals, prime ideals, and completely prime ideals correspond to each other. A list of problems is discussed. In Proposition 3.11 it is proved that the canonical mapping from a right invariant right chain domainRonto the associated right holoid can be extended to a valuation from the skew fieldQ(R)of quotients ofRonto an ordered group if and only ifJa⊆aJfor alla∈RandJ=J(R), the Jacobson radical ofR.
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