Decomposing overrings
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- by B. Cortzen, L. W. Small and J. T. Stafford PDF
- Proc. Amer. Math. Soc. 82 (1981), 28-30 Request permission
Abstract:
We show that if $S \supset R$ are rings such that ${S_R}$ is projective, then ${R_R}$ is a direct summand of ${S_R}$ if and only if ${S_R}$ is faithfully projective (this condition holds, in particular, if ${S_R}$ is free).References
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N. Bourbaki, Algèbre commutative, Chaps. I, II, Hermann, Paris, 1961.
- Barbara Cortzen, Finitistic dimensions of ring extensions, Comm. Algebra 10 (1982), no. 9, 993–1001. MR 654053, DOI 10.1080/00927878208822761
- T. Y. Lam, Serre’s conjecture, Lecture Notes in Mathematics, Vol. 635, Springer-Verlag, Berlin-New York, 1978. MR 0485842
- John C. McConnell, On the global dimension of some rings, Math. Z. 153 (1977), no. 3, 253–254. MR 457498, DOI 10.1007/BF01214478
- J. T. Stafford, On the stable range of right Noetherian rings, Bull. London Math. Soc. 13 (1981), no. 1, 39–41. MR 599638, DOI 10.1112/blms/13.1.39
Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 82 (1981), 28-30
- MSC: Primary 16A50; Secondary 16A62
- DOI: https://doi.org/10.1090/S0002-9939-1981-0603595-6
- MathSciNet review: 603595