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Some examples in PI ring theory

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Abstract

Several examples are constructed, including a finite ring which cannot be embedded in matrices over any commutative ring, a semiprime PI ring with no classical ring of quotients, an example showing that the property of having all regular elements invertible is not inherited by matrix ringsM n(R), and a prime PI ringR with an idempotente such thatR/ReR has finitely generated projective modules not induced by any finitely-generated projective R-module.

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Authors and Affiliations

  1. University of California, 94720, Berkeley, California, U. S. A.

    George M. Bergman

Authors
  1. George M. Bergman
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Additional information

Most of this work was done while the author was a guest of the University of Leeds’ Ring Theory Year (1972–1973), with the support of an Alfred P. Sloan Fellowship, and under the stimulating influence of Lance W. Small.

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Bergman, G.M. Some examples in PI ring theory. Israel J. Math. 18, 257–277 (1974). https://doi.org/10.1007/BF02757282

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  • DOI: https://doi.org/10.1007/BF02757282

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