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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UNIV LONDON QUEEN MARY & WESTFIELD COLL,SCH MATH SCI,LONDON E1 4NS,ENGLANDUNIV LONDON QUEEN MARY & WESTFIELD COLL,SCH MATH SCI,LONDON E1 4NS,ENGLAND