- References
- External links
In rigid analysis, a branch of mathematics, the Tate algebra over a complete ultrametric field k, named for John Tate, is the subring R of the formal power series ring 
consisting of 
such that 
as 
. The maximal spectrum of R is then a rigid-analytic space.
Define the Gauss norm of 
in R by
This makes R a Banach k-algebra.
With this norm, any ideal 
of 
is closed and 
is a finite field extension of ground field 
.
References
- {{citation|author1=Bosch, Siegfried|author2=Güntzer, Ulrich|author3=Remmert, Reinhold|title=Non-archimedean analysis|location=Chapter 5|publisher=Springer|year=1984}}
External links
- http://math.stanford.edu/~conrad/papers/aws.pdf
- https://web.archive.org/web/20060916051553/http://www-math.mit.edu/~kedlaya//18.727/tate-algebras.pdf
1 : Mathematical analysis
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