Picard groups and infinite matrix rings

Authors:
Gene Abrams and Jeremy Haefner

Journal:
Trans. Amer. Math. Soc. **350** (1998), 2737-2752

MSC (1991):
Primary 16A42, 16A64

DOI:
https://doi.org/10.1090/S0002-9947-98-01942-4

MathSciNet review:
1422591

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Abstract | References | Similar Articles | Additional Information

Abstract: We describe a connection between the Picard group of a ring with local units and the Picard group of the unital overring . Using this connection, we show that the three groups , , and are isomorphic for any unital ring . Furthermore, each element of arises from an automorphism of , which yields an isomorphsm between and . As one application we extend a classical result of Rosenberg and Zelinsky by showing that the group is abelian for any commutative unital ring .

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Additional Information

**Gene Abrams**

Affiliation:
Department of Mathematics, University of Colorado, Colorado Springs, Colorado 80933

Email:
abrams@math.uccs.edu

**Jeremy Haefner**

Affiliation:
Department of Mathematics, University of Colorado, Colorado Springs, Colorado 80933

Email:
haefner@math.uccs.edu

DOI:
https://doi.org/10.1090/S0002-9947-98-01942-4

Received by editor(s):
November 16, 1995

Article copyright:
© Copyright 1998
American Mathematical Society