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Proceedings of the American Mathematical Society

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Idempotents in matrix rings


Authors: Christopher Barnett and Victor Camillo
Journal: Proc. Amer. Math. Soc. 122 (1994), 965-969
MSC: Primary 16S50; Secondary 15A99, 16E50
DOI: https://doi.org/10.1090/S0002-9939-1994-1246513-1
MathSciNet review: 1246513
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Abstract: Let R be a commutative, von Neumann regular ring and $ {M_n}(R)$ the ring of $ n \times n$ matrices over R. What are the idempotents in $ {M_n}(R)$ ? Our motivation is to think of R as the sort of ring that occurs in functional analysis, for example a ring of measurable functions. We show how to uniquely write down all idempotents in $ {M_n}(R)$ in terms of arbitrary parameters. The main theorem is stated in language to appeal to an audience wider than algebraists, but in a remark, we give a more refined statement for specialists.


References [Enhancements On Off] (What's this?)

  • [1] C. Barnett and V. Camillo, Idempotents in matrices over commutative von Neumann regular Rings, Comm. Algebra 18 (1990), 3905-3911. MR 1068628 (91h:16020)
  • [2] R. S. Pierce, Modules over commutative von Neumann regular rings, Mem. Amer. Math. Soc., vol. 70, Amer. Math. Soc., Providence, RI, 1967. MR 0217056 (36:151)
  • [3] K. R. Goodearl, Von Neumann regular rings, Pitman, New York, 1978. MR 533669 (80e:16011)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1994-1246513-1
Article copyright: © Copyright 1994 American Mathematical Society

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