Finiteness conditions and infinite matrix rings

For a unital ring R, \mbox{\rm 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 \mbox{\rm RCFM}_\alpha(R) which are equivalent to R being, respectively, Quasi-Frobenius, left artinian, and left noe...

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2006-05, Vol.134 (5), p.1257-1263
Main Authors: DEL RIO, Angel, SIMON, Juan Jacobo
Format: Article
Language:English
Subjects:
Adjoints
Algebra
Associative rings and algebras
Equivalence relation
Exact sciences and technology
Homomorphisms
Infinite sets
Integers
Mathematical induction
Mathematical rings
Mathematics
Matrices
Sciences and techniques of general use
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Summary:For a unital ring R, \mbox{\rm 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 \mbox{\rm RCFM}_\alpha(R) which are equivalent to R being, respectively, Quasi-Frobenius, left artinian, and left noetherian.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-05-08090-1