Abstract
We first tackle certain basic questions concerning the Invariant Basis Number (IBN) property and the universal stably finite factor ring of a direct product of a family of rings. We then consider formal triangular matrix rings and obtain information concerning IBN, rank condition, stable finiteness and strong rank condition of such rings. Finally it is shown that being stably finite is a Morita invariant property.
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References
P. M. Cohn, Some remarks on the invariant basis property, Topology, 5 (1966), 215–228.
K. R. Goodearl, Ring Theory, Nonsingular Rings and Modules, Marcel Dekker (1976).
E. L. Green, On the representation theory of rings in matrix form, Pacific J. Math., 100 (1982), 123–138.
A. Haghany, Hopficity and co-hopficity for Morita contexts, Comm. Algebra, 27 (1999), 477–492.
A. Haghany and K. Varadarajan, Study of formal triangular matrix rings, Comm. Algebra, 27 (1999), 5507–5525.
A. Haghany and K. Varadarajan, Study of modules over formal triangular matrix rings, Journal of Pure and Applied Algebra, 147 (2000), 41–58.
J. Kerr, The power series ring over an Ore domain need not be Ore, J. Algebra, 75 (1982), 175–177.
T. Y. Lam, Lectures on Modules and Rings, Springer Verlag (1998).
W. G. Leavitt, Modules without invariant basis number, Proc. AMS, 8 (1957), 322–328.
P. Malcolmson, On making rings weakly finite, Proc. AMS, 80 (1980), 215–218.
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Haghany, A., Varadarajan, K. IBN and related properties for rings. Acta Math Hung 94, 251–261 (2002). https://doi.org/10.1007/s10474-002-0008-1
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DOI: https://doi.org/10.1007/s10474-002-0008-1