Isomorphisms of row and column finite matrix rings
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- by J. Haefner, A. del Río and J. J. Simón PDF
- Proc. Amer. Math. Soc. 125 (1997), 1651-1658 Request permission
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.References
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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
- MR Author ID: 288713
- Email: adelrio@fcu.um.es
- J. J. Simón
- Affiliation: Department of Mathematics, University of Colorado, Colorado Springs, Colorado 80933
- Email: jsimon@fcu.um.es
- 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
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 1651-1658
- MSC (1991): Primary 16D30, 16S50, 16W20
- DOI: https://doi.org/10.1090/S0002-9939-97-03849-5
- MathSciNet review: 1389521