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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Isomorphisms of row and column
finite matrix rings


Authors: J. Haefner, A. del Río and J. J. Simón
Journal: Proc. Amer. Math. Soc. 125 (1997), 1651-1658
MSC (1991): Primary 16D30, 16S50, 16W20
MathSciNet review: 1389521
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Abstract: This paper investigates the ring-theoretic similarities and the categorical dissimilarities between the ring $RFM(R)$ of row finite matrices and the ring $RCFM(R)$ of row and column finite matrices. For example, we prove that two rings $R$ and $S$ are Morita equivalent if and only if the rings $RCFM(R) $ and $RCFM(S)$ are isomorphic. This resembles the result of V. P. Camillo (1984) for $RFM(R)$. We also show that the Picard groups of $RFM(R)$ and $RCFM(R)$ are isomorphic, even though the rings $RFM(R)$ and $RCFM(R)$ are never Morita equivalent.


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Additional Information

J. Haefner
Affiliation: Department of Mathematics, University of Colorado, Colorado Springs, Colorado 80933
Email: haefner@math.uccs.edu

A. del Río
Affiliation: Department of Mathematics, University of Colorado, Colorado Springs, Colorado 80933
Email: adelrio@fcu.um.es

J. J. Simón
Affiliation: Department of Mathematics, University of Colorado, Colorado Springs, Colorado 80933
Email: jsimon@fcu.um.es

DOI: http://dx.doi.org/10.1090/S0002-9939-97-03849-5
PII: S 0002-9939(97)03849-5
Received by editor(s): January 8, 1996
Additional Notes: This paper was written while the first author was visiting the Universidad de Murcia with a grant from DGICYT (SAB 95-0215)
The second and third authors have been supported by DGICYT (PB-0300-C02-02)
Communicated by: Ken Goodearl
Article copyright: © Copyright 1997 American Mathematical Society