Quadratic forms of dimension 8 with trivial discrimiand and Clifford algebra of index 4

Izhboldin and Karpenko proved in 2000 that any quadratic form of dimension 8 with trivial discriminant and Clifford algebra of index 4 is isometric to the transfer, with respect to some quadratic \'etale extension, of a quadratic form similar to a 2-fold Pfister form. We give a new proof of this result, based on a theorem of decomposability for degree 8 and index 4 algebras with orthogonal involution

Model for fermion mass matrices and the origin of quark-lepton symmetry

Several phenomenological features of fermion masses and mixings can be accounted for by a simple model for fermion mass matrices, which suggests an underlying U(2) horizontal symmetry. In this context, it is also proposed how an approximate quark-lepton symmetry can be achieved without unified gauge theories.Comment: 12 pages, RevTex. Minor changes, some references adde

Leptogenesis and neutrino parameters

We calculate the baryonic asymmetry of the universe in the baryogenesis-via-leptogenesis framework, assuming first a quark-lepton symmetry and then a charged-neutral lepton symmetry. We match the results with the experimentally favoured range. In the first case all the oscillation solutions to the solar neutrino problem, except the large mixing matter solution, can lead to the allowed range, but with fine tuning of the parameters. In the second case the general result is quite similar. Some related theoretical hints are discussed.Comment: RevTex, 21 pages with 8 figure

On the level of principal ideal domains

Baeza, R (Baeza, R.)Univ Talca, Inst Matemat, Talca, ChileWe construct principal ideal domains with level different from the level of their fields of fractions. We also make some remarks on the sublevel of principal ideal domain

Relations in I-n and (IWq)-W-n in characteristic 2

Baeza, R. Instituto de Matemáticas, Universidad de Talca, Casilla 721, Talca, ChileLet K be a field of characteristic 2. We give natural presentations of the subgroups In(K) of the Witt ring W(K) of K and the subgroups InWq(K) of the Witt group Wq(K) of K. Our results generalize the results of Arason and Elman in [J.K. Arason, R. Elman, Powers of the fundamental ideal in the Witt ring, J. Algebra 239 (2001) 150–160], where the characteristic is assumed to be different from 2

On some invariants of fields of characteristic p>0

Baeza, R. Instituto de Matemáticas, Universidad de Talca, Casilla 721, Talca, Chil