Quotient sheaves and valuation rings
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- by Joel Cunningham PDF
- Trans. Amer. Math. Soc. 164 (1972), 227-239 Request permission
Abstract:
In this paper a construction of a quotient sheaf of a sheaf of rings is given. This construction is analogous to the Utumi ring of quotients of a ring. For a valuation ring V, a sheaf of rings corresponding to V is introduced and its quotient sheaf is computed. It is shown that this quotient sheaf corresponds to the completion of V in case V is discrete rank one and that V is maximal if and only if its associated sheaf of rings is its own quotient sheaf.References
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Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 164 (1972), 227-239
- MSC: Primary 16.90; Secondary 13.00
- DOI: https://doi.org/10.1090/S0002-9947-1972-0286845-7
- MathSciNet review: 0286845