Beelen, Peter; Gramlich, Ralf On anti-automorphisms of the first kind in division rings. (English) Zbl 1016.16009 Proc. Am. Math. Soc. 130, No. 12, 3745-3746 (2002). A short proof is given for the well-known fact that a division ring of finite degree over its center that admits an anti-automorphism of the first kind also admits an involutive anti-automorphism. Reviewer: L.A.Bokut’ (Novosibirsk) Cited in 1 Document MSC: 16K20 Finite-dimensional division rings 16W20 Automorphisms and endomorphisms 16W10 Rings with involution; Lie, Jordan and other nonassociative structures Keywords:division rings; anti-automorphisms; involutions PDFBibTeX XMLCite \textit{P. Beelen} and \textit{R. Gramlich}, Proc. Am. Math. Soc. 130, No. 12, 3745--3746 (2002; Zbl 1016.16009) Full Text: DOI References: [1] A.A. Albert, Structure of algebras, American Mathematical Society, New York 1939. · Zbl 0023.19901 [2] P. K. Draxl, Skew fields, London Mathematical Society Lecture Note Series, vol. 81, Cambridge University Press, Cambridge, 1983. · Zbl 0498.16015 [3] Nathan Jacobson, Finite-dimensional division algebras over fields, Springer-Verlag, Berlin, 1996. · Zbl 0874.16002 [4] Max-Albert Knus, Alexander Merkurjev, Markus Rost, and Jean-Pierre Tignol, The book of involutions, American Mathematical Society Colloquium Publications, vol. 44, American Mathematical Society, Providence, RI, 1998. With a preface in French by J. Tits. · Zbl 0955.16001 [5] Louis Halle Rowen, Polynomial identities in ring theory, Pure and Applied Mathematics, vol. 84, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1980. · Zbl 0461.16001 [6] David J. Saltman, Azumaya algebras with involution, J. Algebra 52 (1978), no. 2, 526 – 539. · Zbl 0382.16003 · doi:10.1016/0021-8693(78)90253-3 [7] Winfried Scharlau, Quadratic and Hermitian forms, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 270, Springer-Verlag, Berlin, 1985. · Zbl 0584.10010 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.