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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

The completion of a ring with a valuation


Author: Helen E. Adams
Journal: Proc. Amer. Math. Soc. 36 (1972), 21-25
MSC: Primary 16A80
DOI: https://doi.org/10.1090/S0002-9939-1972-0357519-4
MathSciNet review: 0357519
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Abstract: This paper proves three main results: the completion of a commutative ring with respect to a Manis valuation is an integral domain; a necessary and sufficient condition is given that the completion be a field; and the completion is a field when the valuation is Harrison and the value group is archimedean ordered.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0357519-4
Keywords: Valuation on a ring, valuated ring completion, Manis valuation, Harrison prime
Article copyright: © Copyright 1972 American Mathematical Society