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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Roth's equivalence problem in unit regular rings


Author: Robert E. Hartwig
Journal: Proc. Amer. Math. Soc. 59 (1976), 39-44
MSC: Primary 16A30; Secondary 15A21
MathSciNet review: 0409543
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Abstract: It is shown that for matrices over a unit regular ring $ \left[ {\begin{array}{*{20}{c}} A & C \\ 0 & D \\ \end{array} } \right]\sim\left[ {\begin{array}{*{20}{c}} A & 0 \\ 0 & D \\ \end{array} } \right]$ if and only if there exist solutions $ X$ and $ Y$ to $ AX - YD = C$, thus providing a partial generalization to Roth's theorem.


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DOI: https://doi.org/10.1090/S0002-9939-1976-0409543-4
Article copyright: © Copyright 1976 American Mathematical Society