Homomorphisms and Involutions of Unramified Henselian Division Algebras

Autor:	Sergey V. Tikhonov, V. I. Yanchevskii
Rok vydání:	2015
Předmět:	Statistics and Probability Pure mathematics Inner automorphism Residue field Applied Mathematics General Mathematics Bijection Bibliography Equivalence relation Homomorphism Mathematics
Zdroj:	Journal of Mathematical Sciences. 209:657-664
ISSN:	1573-8795 1072-3374
Popis:	Let K be a Henselian field with a residue field $$ \overline{K} $$ , and let A1, A2 be finite-dimensional division unramified K-algebras with residue algebras Ā 1 and Ā 2 Further, let HomK(A1,A2) be the set of nonzero K-homomorphisms from A1 to A2. It is proved that there is a natural bijection between the set of nonzero $$ \overline{K} $$ -homomorphisms from Ā 1 to Ā 2 and the factor set of HomK and the factor set of HomK(A1,A2) under the equivalence relation: ϕ 1 ∼ ϕ 2 ⇔ there exists m ∈ 1 +MA2 such that ϕ2 = ϕ1 im, where im is the inner automorphism of A2 induced by m. A similar result is obtained for unramified algebras with involutions. Bibliography: 7 titles.
Databáze:	OpenAIRE
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