Isomorphisms of row and column finite matrix rings
Del Rio, A.
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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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