Isomorphism of Qf Algebras Over ℚ

Abstract

We show that the local-global principle (Hasse principle) holds for isomorphisms between commutative local QF algebras over Q of dimension five with radical cubed zero, and obtain a criterion for them to be isomorphic by the Hilbert symbol or the Legendre symbol. As a consequence, we give the isomorphism classes of some type of local algebras over Q by using a factor group of Q * .