Tamely ramified fields

Let K be a field with a (non-trivial) discrete valuation v. The valuation ring (resp. residue field, resp. value group) is denoted by 

Let L denote a finite, separable extension of K. It is well-known that there are only finitely many- inequivalent - extensions of v to L and each of these extensions is again a discrete valuation (see for instance [3], Alg.Comm., chap.6, 8,Th.l and cor.3 of prop.l no l). 

Definition 2.1.2. A finite separable extension L of K is said to be tamely ramified over K with respect to v (shortly, if there is no danger of confusions L is tame over K) if for each extension w of v to L we have 

Lemma 2.1.3. In the following L, L etc., denote fields containing K if a compositum is considered then it is tacitely assumed that both are contained in an overfield.  

Ln K tame 4= LsK tame and LnL tame with respect to every extension w of v to L. 

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