Abstract: In these notes we prove that: (i) any Galois cubic extension of the field Q of the rational numbers is of the form Q(9) = Q[X]/(fX)) with EX) = = nc G=2cosT, for some TES); (ii) for EX) = x2)- 3X — G the extension Q(f) is Galois: = G ES - 21 E am dE jp iff for T'=arccos(+ ) and r, "+55 one has G; 2 cosT EQ, j=0,1,2; (ii) if the extension Q (f) is non trivial it is of the form Q(cos y) and cosY|» cosYy9 E Q(cos7 where y= + and Y; =y+) 2 j=0,1,2; Q(f) is trivial iff all cost; E Q and in this case 3 Q(f) = Q x Q x Q; (iv) the collection of all these extensions is parametrized by non-zero elements of the ring Z[ w], where w= — + + a 1EC; (v) the natural generators of the Harrison group T(Z3,Q ) are indexed by « and those rational primes that satisfy p=1 (mod 3) Ver menos