The completion of a ring with a valuation
HTML articles powered by AMS MathViewer
- by Helen E. Adams
- Proc. Amer. Math. Soc. 36 (1972), 21-25
- DOI: https://doi.org/10.1090/S0002-9939-1972-0357519-4
- PDF | Request permission
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.References
- Helen E. Adams, Filtrations and valuations on rings, Pacific J. Math. 43 (1972), 7–14. MR 318240
- D. K. Harrison, Finite and infinite primes for rings and fields, Mem. Amer. Math. Soc. 68 (1966), 62. MR 207735
- Merle E. Manis, Valuations on a commutative ring, Proc. Amer. Math. Soc. 20 (1969), 193–198. MR 233813, DOI 10.1090/S0002-9939-1969-0233813-2
Bibliographic Information
- © Copyright 1972 American Mathematical Society
- 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