Let ∧ be a ring endowed with an involution a-> a~. We say that two units a and b of ∧ fixed under the involution are congruent if there exists an element u implied by ∧ ~x such that a = ubu~. We denote by H(∧) the set of congruence classes.In this paper we consider the question of whether the natural map H(∧) -> H(A) induced by inclusion is injective. We give sufficient conditions on the order ∧ for this map to be injective and give applications to hermitian forms over group rings.
展开▼
