Derivations nilpotent on subsets of prime rings |
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Authors: | Charles Lanski |
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Institution: | Department of Mathematics , University of Southern California , Los Angeles, 90089-1113, California |
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Abstract: | ABSTRACT Let D be a division algebra with center F. Consider the group CK 1(D) = D*/F*D′ where D* is the group of invertible elements of D and D′ is its commutator subgroup. In this note we shall show that, assuming a division algebra D is a product of cyclic algebras, the group CK 1(D) is trivial if and only if D is an ordinary quaternion algebra over a real Pythagorean field F. We also characterize the cyclic central simple algebras with trivial CK 1 and show that CK 1 is not trivial for division algebras of index 4. Using valuation theory, the group CK 1(D) is computed for some valued division algebras. |
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Keywords: | Division algebras Reduced K-theory |
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