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Ore Extensions over Total Valuation Rings

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Abstract

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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  1. Faculty of Engineering, Tokushima Bunri University, Sanuki, Kagawa, 769-2193, Japan

    Hidetoshi Marubayashi

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  1. Hidetoshi Marubayashi
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Correspondence to Hidetoshi Marubayashi.

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Marubayashi, H. Ore Extensions over Total Valuation Rings. Algebr Represent Theor 13, 607–622 (2010). https://doi.org/10.1007/s10468-009-9139-4

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  • DOI: https://doi.org/10.1007/s10468-009-9139-4

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