THE GENERALIZED EISENSTEIN CRITERION
<正> The Eisenstein Criterion is a sharp tool, i.e. a sufficient condition to judge a polynomial irreducible by using the coefficients of the polynomial. In particular, it plays an important role in studying totally ramified extensions of local fields. In this report, we shall generalize the Eisenstein Criterion for totally ramified extensions of local fields, and then we can get some results about extensions of local fields, that is to say, the conditions of tamely ramified extensions are cyclic or metacyclic.