Riassunto
Un anello separato filtrato ha una immediata estensione massimale completa. Questo risultato è un analogo del teorema di Krull della teoria degli anelli di valutazione nell’ambito degli anelli filtrati.
Summary
A separated filtered ring has a maximally complete immediate extension. This is an analogue of Krull Theorem from valuation ring theory in the frame of filtered rings.
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References
J. Becker—J. Denef—L. Lipshitz—L. Van Den Dries,Ultraproducts and approximation in local rings I, Inventiones Math.,51 (1979), pp. 189–203.
I. Kaplansky,Maximal fields with valuations, Duke Math. J.,9 (1942), pp 303–321.
W. Krull,Allgemeine Bewertungstheorie, J. für Math.,167 (1932) pp. 160–196.
H. Matsumura,Commutative Algebra, Benjamin, New York (1980).
V. Nica—D. Popescu,A Structure Theorem on Formally Smooth Morphisms in Positive Characteristic, J. Algebra,100 (1986), pp. 436–455.
A. Ostrowski,Untersuchungen zur arithmetische Theorie der Körper II, III, Math. Z.,39 (1935), pp. 321–404.
D. Popescu,On Zariski’s uniformization theorem, Spring Verlag Lecture Notes in Math.,1056 (1984), pp. 264–297.
D. Popescu,Algebraic extensions of valued fields, J. of Algebras,108 (1987), pp. 513–533.
P. Ribenboim,Théorie des Valuations, University Press, Montréal (1964).
O. F. G. Schilling,The Theory of Valuations, Amer. Math. Soc., New York (1970).
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Morariu, W., Popescu, D. Immediate extensions of filtered rings. Ann. Univ. Ferrara 35, 35–57 (1989). https://doi.org/10.1007/BF02825208
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DOI: https://doi.org/10.1007/BF02825208