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Proceedings of the American Mathematical Society

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A characterization of regular local rings

Author: Jacob Barshay
Journal: Proc. Amer. Math. Soc. 29 (1971), 437-439
MSC: Primary 13.95
MathSciNet review: 0279093
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Abstract: For a local ring, $ (A,\mathfrak{M})$ of positive depth regularity is shown to be equivalent to the symmetric algebra of $ \mathfrak{M}$ being torsion free.

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

  • [1] Artibano Micali, Sur les algèbres universelles, Ann. Inst. Fourier (Grenoble) 14 (1964), no. fasc. 2, 33–87 (French). MR 0177009
  • [2] A. Micali, P. Salmon, and P. Samuel, Intégrité et factorialité des algèbres symétriques, Proc. Fourth Brazilian Math. Colloq. (1963) (Portuguese), Conselho Nacional de Pesquisas, São Paulo, 1965, pp. 61–76 (French). MR 0207741
  • [3] D. G. Northcott, Ideal theory, Cambridge Tracts in Mathematics and Mathematical Physics, No. 42, Cambridge, at the University Press, 1953. MR 0058575
  • [4] Pierre Samuel, Anneaux gradués factoriels et modules réflexifs, Bull. Soc. Math. France 92 (1964), 237–249 (French). MR 0186702

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Keywords: Regular local ring, symmetric algebra, Rees algebra
Article copyright: © Copyright 1971 American Mathematical Society