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. Gersten,*The localization theorem for projective modules*, Comm. Algebra**2**(1974), 307-350. MR**0357547 (50:10015)****[2]**D. Grayson,*K-theory of hereditary categories*, J. Pure Appl. Algebra**11**(1978), 67-74. MR**0476833 (57:16385)****[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]**I. Kaplansky,*Fields and rings*, 2nd ed., Univ. of Chicago Press, Chicago, 1972. MR**0349646 (50:2139)**

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

Article copyright:
© Copyright 1979
American Mathematical Society