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

 

Finiteness conditions and infinite matrix rings


Authors: Ángel del Río and Juan Jacobo Simón
Journal: Proc. Amer. Math. Soc. 134 (2006), 1257-1263
MSC (2000): Primary 16S50; Secondary 16P20, 16P40
Published electronically: October 4, 2005
MathSciNet review: 2199167
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Abstract: For a unital ring $ R$, RCFM$ _\alpha (R)$ denotes the ring of row and column finite matrices over $ R$ indexed by $ \alpha$. We give necessary and sufficient structural conditions on RCFM$ _\alpha(R)$ which are equivalent to $ R$ being, respectively, Quasi-Frobenius, left artinian, and left noetherian.


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Additional Information

Ángel del Río
Affiliation: Departamento de Matemáticas, Universidad de Murcia, 30100 Murcia, Spain
Email: adelrio@um.es

Juan Jacobo Simón
Affiliation: Departamento de Matemáticas, Universidad de Murcia, 30100 Murcia, Spain
Email: jsimon@um.es

DOI: http://dx.doi.org/10.1090/S0002-9939-05-08090-1
PII: S 0002-9939(05)08090-1
Received by editor(s): September 2, 2004
Received by editor(s) in revised form: November 19, 2004
Published electronically: October 4, 2005
Additional Notes: Both authors were partially supported by the D.G.I. of Spain and Fundación Séneca of Murcia
Communicated by: Martin Lorenz
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.