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Finite-dimensional right duo algebras are duo

1982
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Proceedings of the American Mathematical Society
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Available examples of right (but not left) duo rings include rings without unity element which are two dimensional algebras over finite prime fields. We prove that a right duo ring with unity element which is a finite dimensional algebra over an arbitrary field A' is a duo ring. This result is obtained as a corollary of a theorem on right duo, right artinian rings R with unity: left duo-ness is equivalent to each right ideal of R having equal right and left composition lengths, which is

doi:10.1090/s0002-9939-1982-0637159-6
fatcat:52imz2vqybgybjnl4sa4k67mpa