Grenier-Boley, NicolasLequeu, EmmanuelMahmoudi, Mohammad Gholamzadeh2010-11-302010-11-302010-11-30200810.1142/S021949880800303Xhttps://infoscience.epfl.ch/handle/20.500.14299/60920WOS:000260274700001Let K be a field of characteristic different from 2. It is known that a quadratic Pfister form over K is hyperbolic once it is isotropic. It is also known that the dimension of an anisotropic quadratic form over K belonging to a given power of the fundamental ideal of the Witt ring of K is lower bounded. In this paper, weak analogues of these two statements are proved for hermitian forms over a multiquaternion algebra with involution. Consequences for Pfister involutions are also drawn. An invariant u(alpha) of K with respect to a nonzero pure quaternion of a quaternion division algebra over K is defined. Upper bounds for this invariant are provided. In particular an analogue is obtained of a result of Elman and Lam concerning the u-invariant of a field of level at most 2.Hermitian formPfister formmultiquaternion algebra with involutionPfister involutionu-invariantInvolutionAlgebrasLeveltext::journal::journal article::research article