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Roth's theorems over commutative rings

By William H. Gustafson

Abstract

AbstractIn 1952, W.E. Roth showed that matrix equations of the forms AX−YB = C and AX−XB = C over fields can be solved if and only if certain block matrices built from A, B, and C are equivalent or similar. We show here that these criteria remain valid over arbitrary commutative rings. To do this, we use standard commutative algebra methods to reduce to the case of Artinian rings, where a simple argument wit

Publisher: Published by Elsevier Inc.
Year: 1979
DOI identifier: 10.1016/0024-3795(79)90106-X
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