Isomorphisms of row and column finite matrix rings
Abstract
This paper investigates the ring-theoretic similarities and the cate-
gorical dissimilarities between the ring RFM(R) of row finite matrices and the
ring RCFM(R) of row and column finite matrices. For example, we prove that
two rings R and S are Morita equivalent if and only if the rings RCFM(R)
and RCFM(S) are isomorphic. This resembles the result of V. P. Camillo
(1984) for RFM(R). We also show that the Picard groups of RFM(R) and
RCFM(R) are isomorphic, even though the rings RFM(R) and RCFM(R)
are never Morita equivalent.
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