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Proceedings of the American Mathematical Society

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$ K$-theory of commutative regular rings


Author: Andy R. Magid
Journal: Proc. Amer. Math. Soc. 39 (1973), 489-492
MSC: Primary 13D15
DOI: https://doi.org/10.1090/S0002-9939-1973-0311650-9
Erratum: Proc. Amer. Math. Soc. 46 (1974), 455.
MathSciNet review: 0311650
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Abstract: Pierce's representation of a commutative regular ring as a sheaf of fields is used to compute the $ K$-theory of the ring: $ {K_1}$ is units (Robert's Theorem) and $ {K_2}$ is generated by symbols.


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

  • [1] M. Artin, Algebraic approximation of structures over complete local rings, Inst. Hautes Études Sci. Publ. Math. 36 (1969), 23-58. MR 42 #3087. MR 0268188 (42:3087)
  • [2] A. Magid, Pierce's representation and separable algebras, Illinois J. Math. 15 (1971), 114-121. MR 42 #7713. MR 0272832 (42:7713)
  • [3] J. Milnor, Introduction to algebraic $ K$-theory, Ann. of Math. Studies, no. 72, Princeton Univ. Press, Princeton, N.J., 1971. MR 0349811 (50:2304)
  • [4] R. Pierce, Modules over commutative regular rings, Mem. Amer. Math. Soc. No. 70 (1967). MR 36 #151. MR 0217056 (36:151)
  • [5] L. Roberts, $ {K_1}$ of a commutative von Neumann regular ring, Proc. Amer. Math. Soc. 32 (1972), 425-426. MR 0289497 (44:6686)
  • [6] O. Villamayor and D. Zelinsky, Galois theory with infinitely many idempotents, Nagoya Math. J. 35 (1969), 83-98. MR 39 #5555. MR 0244238 (39:5555)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0311650-9
Keywords: $ K$-theory, von Neumann regular ring, functor of finite type
Article copyright: © Copyright 1973 American Mathematical Society

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