Finiteness conditions and infinite matrix rings

del Río, Ángel; Simón, Juan

doi:10.1090/S0002-9939-05-08090-1

Finiteness conditions and infinite matrix rings
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by Ángel del Río and Juan Jacobo Simón

Proc. Amer. Math. Soc. 134 (2006), 1257-1263

DOI: https://doi.org/10.1090/S0002-9939-05-08090-1

Published electronically: October 4, 2005

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Abstract:

For a unital ring $R$, $\mathrm {RCFM}_\alpha (R)$ denotes the ring of row and column finite matrices over $R$ indexed by $\alpha$. We give necessary and sufficient structural conditions on $\mathrm {RCFM}_\alpha (R)$ which are equivalent to $R$ being, respectively, Quasi-Frobenius, left artinian, and left noetherian.

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