Let IV(F) denote the Mitt ring of nondegenerate symmetric bilinear forms over a field F. In this paper wc shall be concerned only with formally real fields, for which we write Wr,,l(F) ~mm W(F)/Wil W(F) for the reduced R’itt ring. In [13, 141 the rings W(F) and iTred are shown to be special cases of absfrart lWtt rirqs and a great deal of the ring structure is developed in this setting. In [6] ...

We show that the odd-indexed derived Witt groups of a semilocal ring with trivial involution vanish. We show that this is wrong when the involution is not trivial and we provide examples.

In this paper the Poincaré–Birkhoff–Witt (PBW) rings are characterized. Gröbner bases techniques are also developed for these rings. An explicit presentation of Exti (M,N) is provided when N is a centralizing bimodule. Mathematics Subject Classifications (2000): 16Z05, 16E30.