ISOMORPHISMS OF ROW AND COLUMN FINITE MATRIX-RINGS

This paper investigates the ring-theoretic similarities and the catego rical dissimilarities between the ring RFM(R) of row finite matrices a nd 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 o f 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) an d RCFM(R) are never Morita equivalent.