Homomorphisms and involutions of unramified henselian division algebras

被引：0

作者：

Tikhonov S.V. ^{[1
]}

Yanchevskii V.I. ^{[2
]}

机构：

[1] Belarus State University, Minsk

[2] The Institute of Mathematics, Belarus National Academy of Sciences, Minsk

来源：

Journal of Mathematical Sciences | 2015年 / 209卷 / 4期

关键词：

Division Algebra; Central Simple Algebra; Central Division; Identity Automorphism; Ring Versus;

D O I：

10.1007/s10958-015-2519-x

中图分类号：

学科分类号：

摘要：

Let K be a Henselian field with a residue field (Formula presented.), and let A1, A2 be finite-dimensional division unramified K-algebras with residue algebras Ā1 and Ā2. Further, let HomK(A1,A2) be the set of nonzero (Formula presented.)-homomorphisms from A1 to A2. It is proved that there is a natural bijection between the set of nonzero K-homomorphisms from A1 to A2 and the factor set of HomK(A1,A2) under the equivalence relation: (Formula presented.) there exists m ∈ 1 +MA2 such that (Formula presented.), where im is the inner automorphism of A2 induced by m. A similar result is obtained for unramified algebras with involutions. © 2015 Springer Science+Business Media New York.

引用

页码：657 / 664

页数：7

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