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Von Neumann's Manuscript on Inductive Limits of Regular Rings
Published online by Cambridge University Press: 20 November 2018
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It is now known (3) that if is a regular rank ring, then the rank function can be extended to the matrix ring in such a way that R(a) = R(a ꕕ n) ; here, a is an arbitrary element of is the n × n diagonal matrix with a for each entry on the diagonal, and R denotes rank in and also in . It is also known (2) that every regular rank ring has a rankmetric completion which is again a regular rank ring.
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- Copyright © Canadian Mathematical Society 1968
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