Nonstandard theory of Zariski rings
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- by Loren C. Larson PDF
- Proc. Amer. Math. Soc. 29 (1971), 23-29 Request permission
Abstract:
Let $^ \ast R$ be an enlargement (in the sense of A. Robinson) of a Zariski ring (R, A), let $\mu$ be the monad of zero in $^ \ast R$ when R is given the A-adic topology and set ${R_\mu }$ equal to the quotient ring $^ \ast R/\mu$. It is shown that $(R,{R_\mu })$ is a flat couple, and ${R_\mu }$ is Noetherian if and only if it is semilocal. Furthermore, if R is semilocal and A is the (Jacobson) radical then ${R_\mu }$ is semilocal, with the same number of maximal ideals and the same (Krull) dimension as R.References
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Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 29 (1971), 23-29
- MSC: Primary 13.25; Secondary 02.00
- DOI: https://doi.org/10.1090/S0002-9939-1971-0279082-8
- MathSciNet review: 0279082