Ore Extensions over Total Valuation Rings

It is shown that any Ore extension R  =  V [ x ; σ , δ ] over a total valuation ring V is always v-Bezout which is a generalization of commutative GCD domains. By using this result, a necessary and sufficient condition are given for R to be fully left bounded.

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Bibliographic Details
Published inAlgebras and representation theory Vol. 13; no. 5; pp. 607 - 622
Main Author Marubayashi, Hidetoshi
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.10.2010
Subjects
Associative Rings and Algebras
Commutative Rings and Algebras
Mathematics
Mathematics and Statistics
Non-associative Rings and Algebras
16W60
Total valuation ring
Ore extension
Commutative GCD domain
16L99
16S36
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Summary:It is shown that any Ore extension R  =  V [ x ; σ , δ ] over a total valuation ring V is always v-Bezout which is a generalization of commutative GCD domains. By using this result, a necessary and sufficient condition are given for R to be fully left bounded.
ISSN:1386-923X
1572-9079
DOI:10.1007/s10468-009-9139-4