Ore Extensions over Total Valuation Rings

• Published in: Algebras and representation theory Vol. 13; no. 5; pp. 607 - 622
• Main Author: Marubayashi, Hidetoshi
• Format: Journal Article
• Language: English
• 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

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.