Quadratic and \(\lambda\)-Hermitian forms
The author gives algebro-topological conditions for a unitary subring A of a topological ring B to have, up to isomorphism, the same quadratic or \(\lambda\)-Hermitian forms as B. These conditions are formulated for a topological ring R in terms of the topology of R, together with an involution, and an element, \(\lambda\), in the center of R. For \(\lambda =1\) and the trivial involution, the above condition has been used by \textit{R. G. Swan} [Trans. Am. Math. Soc. 230, 201-234 (1977; Zbl 0443.13005)] in the study of the relationship between isomorphism classes of finitely generated projective modules over A and over B, respectively. The examples in the paper concern the ring C(X,k) of continuous k-valued functions on a topological space X \((k={\mathbb{R}}\), \({\mathbb{C}}\) or \({\mathbb{H}})\). In the reviewer's opinion the author should have indicated the topology that he considered in these rings, because in cases where X is not compact there are several choices.
scientific article; zbMATH DE number 4127309