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Isomorphisms of Row and Column Finite Matrix Rings
J. Haefner, A. Del Río and J. J. Simón
Proceedings of the American Mathematical Society
Vol. 125, No. 6 (Jun., 1997), pp. 1651-1658
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2162204
Page Count: 8
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This paper investigates the ring-theoretic similarities and the categorical 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.
Proceedings of the American Mathematical Society © 1997 American Mathematical Society