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Maximal immediate extensions are not necessarily maximally complete

Part of: General commutative ring theory

Published online by Cambridge University Press:  09 April 2009

Hans Heinrich Brungs  and
Günter Törner
Hans Heinrich Brungs
Affiliation:
University of Alberta Edmonton, AlbertaCanadaT6G 2G1
Günter Törner
Affiliation:
Fachbereich Mathematik Universität DuisburgD 4100 Duisburg, Federal Republic of Germany
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Abstract

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An extension R1 of a right chain ring R is called immediate if R1 has the same residue division ring and the same lattice of principal right ideals as R. Properties of such immediate extensions are studied. It is proved that for every R, maximal immediate extensions exist, but that in contrast to the commutative case maximal right chain rings are not necessarily linearly compact.

Keywords

maximal valuation ringcompletionright chain ring

MSC classification

Secondary: 13A18: Valuations and their generalizations
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 49 , Issue 2 , October 1990 , pp. 196 - 211
Copyright
Copyright © Australian Mathematical Society 1990

References

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