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2 results

Dependent Automorphisms in Prime Rings
Matej Brešar, W. S. Martindale, 3rd, C. Robert Miers
Journal: Canadian Mathematical Bulletin / Volume 41 / Issue 4 / 01 December 1998
Published online by Cambridge University Press: 20 November 2018, pp. 452-462
Print publication: 01 December 1998
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For each $n\ge 4$ we construct a class of examples of a minimal $C$-dependent set of $n$ automorphisms of a prime ring $R$, where $C$ is the extended centroid of $R$. For $n=4$ and $n=5$ it is shown that the preceding examples are completely general, whereas for $n=6$ an example is given which fails to enjoy any of the nice properties of the above example.

Nilpotent Inner Derivations of the Skew Elements of Prime Rings With Involution
W. S. Martindale, 3rd, C. Robert Miers
Journal: Canadian Journal of Mathematics / Volume 43 / Issue 5 / 01 October 1991
Published online by Cambridge University Press: 20 November 2018, pp. 1045-1054
Print publication: 01 October 1991
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Let R be a prime ring with invoution *, of characteristic 0, with skew elements K and extended centroid C. Let a ∈ K be such that (ad a)n =0 on K. It is shown that one of the following possibilities holds: (a) R is an order in a 4-dimensional central simple algebra, (b) there is a skew element λ in C such that , (c) * is of the first kind, n ≡ 0 or n ≡ 3 (mod 4), and . Examples are given illustrating (c).