Row and column finite matrices
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Abstract:
Consider the ring of all $\kappa \times \kappa$ column finite matrices over a ring $R$. We prove that each such matrix is conjugate to a row and column finite matrix if and only if $R$ is right Noetherian and $\kappa$ is countable. We then demonstrate that one can perform this conjugation on countably many matrices simultaneously. Some applications and limitations are given.References
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Additional Information
- Pace P. Nielsen
- Affiliation: Department of Mathematics, University of California, Berkeley, California 94720
- MR Author ID: 709329
- Email: pace_nielsen@hotmail.com
- Received by editor(s): November 19, 2005
- Received by editor(s) in revised form: May 12, 2006
- Published electronically: February 9, 2007
- Communicated by: Martin Lorenz
- © Copyright 2007 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 135 (2007), 2689-2697
- MSC (2000): Primary 16S50; Secondary 16P40
- DOI: https://doi.org/10.1090/S0002-9939-07-08790-4
- MathSciNet review: 2317941