Az Eszterházy Károly Tanárképző Főiskola Tudományos Közleményei. 1993. Sectio Mathematicae. (Acta Academiae Paedagogicae Agriensis : Nova series ; Tom. 21)

A. Grytczuk and J. Kacierzynski: On Factorization in real quadratic number fields

A. GRYTCZUK and J. KACIERZYNSKI ON FACTORIZATION IN REAL QUADRATIC NUMBER FIELDS ABSTRACT: This paper investigates uniqeness of factorization in quadratic number fields. It is proved by elementary method, that under certain conditions, the ring R

k of a field K is the ring with nonuique factorization. 1. Introduction. Using class-field theory C. S. Herz [1] proved the following result Let K = Q(jd) be given quadratic number field with the discriminant D which has / distinct prime divisors. Then the class group H(K) of K hast t -1 even invariants, except the case when K is real and at least one prime p = 3 (mod 4) is ramified, in this case H(K) has t - 2 even invariants. From this result we can deduce that if h- H(K)-\ where K = Q{jd) and <*>0then (1.1) d = p,2q or qr where p is prime and q = r = 3(mod 4) are primes. 81