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

DOI:
https://doi.org/10.1090/S0002-9939-97-03849-5

MathSciNet review:
1389521

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Abstract | References | Similar Articles | Additional Information

Abstract: This paper investigates the ring-theoretic similarities and the categorical dissimilarities between the ring of row finite matrices and the ring of row and column finite matrices. For example, we prove that two rings and are Morita equivalent if and only if the rings and are isomorphic. This resembles the result of V. P. Camillo (1984) for . We also show that the Picard groups of and are isomorphic, even though the rings and are never Morita equivalent.

**1.**G.D. Abrams, Infinite matrix types which determine Morita equivalence. Arch. Math. (**46**), 1986, 33-37. MR**87f:16015****2.**G. Abrams and J. Haefner, Picard groups and infinite matrix rings. Trans. Amer. Math. Soc., to appear.**3.**V.P. Camillo, Morita equivalence and infinite matrix rings. Proc. Amer. Math. Soc. (2)(**90**), 1984, 186-188. MR**85a:16045****4.**L. Fuchs,*Infinite abelian groups*, Vol. II, Acad. Press, New York, 1973. MR**50:2362****5.**J.L. García, The Characterization problem for endomorphism rings. J. Austral Math. Soc. (Series A) (**50**) 1991, 116-137. MR**92a:16035****6.**J. J. Simón, Morita equivalent row finite matrix rings are isomorphic, J. Algebra, (**173**) 1995, 390-393. MR**96d:16012**

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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:
https://doi.org/10.1090/S0002-9939-97-03849-5

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