Wada, Hideo “Hasse principle” for \(\text{GL}_n(D)\). (English) Zbl 0967.20027 Proc. Japan Acad., Ser. A 76, No. 3, 44-46 (2000). Let \(D\) be a Euclidean ring, \(n\in\mathbb{N}\) and \(\text{GL}_n(D)\) the \(n\)-th general linear group over \(D\). If \(f\) is an endomorphism of \(\text{GL}_n(D)\) which preserves conjugacy classes then \(f\) is already an inner automorphism. Reviewer: Gerhard Rosenberger (Dortmund) Cited in 2 Documents MSC: 20G35 Linear algebraic groups over adèles and other rings and schemes 20E36 Automorphisms of infinite groups 20H10 Fuchsian groups and their generalizations (group-theoretic aspects) Keywords:Hasse principle; Euclidean rings; general linear groups; endomorphisms; conjugacy classes; inner automorphisms × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Hua, L. K.: Introduction to Number Theory. Springer-Verlag, New York, pp. 371-382 (1982). [2] Ono, T.: “Hasse principle” for \(GL_2(D)\). Proc. Japan Acad., 75A , 141-142 (1999). · Zbl 0968.20024 · doi:10.3792/pjaa.75.141 [3] Wada, H.: “Hasse principle” for \(SL_n(D)\). Proc. Japan Acad., 75A , 67-69 (1999). · Zbl 1041.11025 · doi:10.3792/pjaa.75.67 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.