O bazie fundamentalnej ciała cyklotomicznego

Abstract

Using a lemma formulated below the author gives a simple proof that 1, t s_1, s = cp (pn), is an integral basis of the field Q (£), where C is a primitive root of unity of degree pn. LEMMA. I f 0 is a root of an Eisenstein polynomial with respect to the prime number p, then p does not divite the index (O : M ) of the order M = < 1, 0 ....0™-1 > in the maximal order O of the field Q (0 ). This lemma appears as a problem in [1], p. 129.