HOMOMORPHISMS AND INVOLUTIONS OF UNRAMIFIED HENSELIAN DIVISION ALGEBRAS

摘要

Let K be a Henselian field with a residue field K, and let A_1, A_2 be finite-dimensional division unramified K-algebras with residue algebras A_1 and A_2- Further, let Hom_K(A_1, A_2) be the set of nonzero K-homomorphisms from A_1 to A_2. It is proved that there is a natural bisection between the set of nonzero K-homomorphisms from A_1 to A_2 and the factor set of Hom_K(A_1, A_2) under the equivalence relation: φ_1 ～ φ_2 = there exists m ∈ 1 + M_(A_2) such that φ_2 = φ_(1im), where i_m is the inner automorphism of A_2 induced by m. A similar result is obtained for unramified algebras with involutions. Bibliography: 7 titles.