in a finite extension of C((x)) is of the form (cf. Puiseux series)

Equivalent definitions

Let B be a ring, and let A be a subring of B. Given an element b in B, the following conditions are equivalent:
:(i) b is integral over A;
:(ii) the subring A[b] of B generated by A and b is a finitely generated ''A''-module;
:(iii) there exists a subring C of B containing A[b] and which is a finitely generated A-module;
:(iv)

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