A note on nonfinitely generated projective -modules

Author:
Takeo Akasaki

Journal:
Proc. Amer. Math. Soc. **86** (1982), 391

MSC:
Primary 16A26; Secondary 16A50, 20C05

MathSciNet review:
671200

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Abstract: Let be a finite group and be its integral group ring. It is shown that if is not solvable, then there exists a nonfinitely generated projective -module which is not free.

**[1]**Takeo Akasaki,*Idempotent ideals in integral group rings*, J. Algebra**23**(1972), 343–346. MR**0304420****[2]**P. A. Linnell,*Nonfree projective modules for integral group rings*, Bull. London Math. Soc.**14**(1982), no. 2, 124–126. MR**647193**, 10.1112/blms/14.2.124**[3]**K. W. Roggenkamp,*Integral group rings of solvable finite groups have no idempotent ideals*, Arch. Math. (Basel)**25**(1974), 125–128. MR**0342549****[4]**Richard G. Swan,*The Grothendieck ring of a finite group*, Topology**2**(1963), 85–110. MR**0153722****[5]**James M. Whitehead,*Projective modules and their trace ideals*, Comm. Algebra**8**(1980), no. 19, 1873–1901. MR**588450**, 10.1080/00927878008822551

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DOI:
https://doi.org/10.1090/S0002-9939-1982-0671200-X

Article copyright:
© Copyright 1982
American Mathematical Society