Tate algebra

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 ${\displaystyle k[[t_{1},...,t_{n}]]}$ consisting of ${\displaystyle \sum a_{I}t^{I}}$ such that ${\displaystyle |a_{I}|\to 0}$ as ${\displaystyle I\to \infty }$. The maximal spectrum of R is then a rigid-analytic space.

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