Pseudo‐quadratic modules over simple‐artinian rings with involution

Let be a simple‐artinian ring with involution. This means that is isomorphic to a matrix ring over a ring that is either a skew field or the direct sum of a skew field and its opposite, and is given in terms of an involution of . We show that an arbitrary pseudo‐quadratic module defined over can be obtained by a tensor product construction from a pseudo‐quadratic module defined over and we apply this result to give a uniform description of arbitrary pseudo‐maximal parabolic subgroups of arbitrary classical groups in terms of pseudo‐quadratic modules.