A note on the localization theorem for projective modules

Author:
Clayton Sherman

Journal:
Proc. Amer. Math. Soc. **75** (1979), 207-208

MSC:
Primary 18F25

DOI:
https://doi.org/10.1090/S0002-9939-1979-0532136-8

MathSciNet review:
532136

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Abstract: Let *R* be a ring and *S* a central multiplicative subset. An example is given to show that the localization theorem for projective modules, valid when *S* consists of non-zero-divisors, does not hold when *S* is allowed to contain zero-divisors.

**[1]**S. M. Gersten,*The localization theorem for projective modules*, Comm. Algebra**2**(1974), 317–350. MR**0357547**, https://doi.org/10.1080/00927877408822015**[2]**Daniel R. Grayson,*The 𝐾-theory of hereditary categories*, J. Pure Appl. Algebra**11**(1977/78), no. 1-3, 67–74. MR**0476833**, https://doi.org/10.1016/0022-4049(77)90041-X**[3]**-,*Higher algebraic K-theory*: II (*after Quillen*), Algebraic*K*-Theory (Evanston, 1976), Lecture Notes in Math., vol. 551, Springer-Verlag, New York, 1976.**[4]**Irving Kaplansky,*Fields and rings*, 2nd ed., The University of Chicago Press, Chicago, Ill.-London, 1972. Chicago Lectures in Mathematics. MR**0349646**

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DOI:
https://doi.org/10.1090/S0002-9939-1979-0532136-8

Article copyright:
© Copyright 1979
American Mathematical Society