Abstract
We show that if Γ is a finitely generated abelian group, then every stably free module over Z[Γ] is free.
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References
H. Bass, Algebraic K-Theory, Benjamin 1968.
Bass H., Murthy M.P.: Grothendieck groups and Picard groups of abelian group rings,. Ann. of Math 86, 16–73 (1967)
N. Bourbaki, Commutative Algebra, Addison-Wesley, 1972.
C.W. Curtis and I. Reiner, Methods of Representation Theory, vol. II. Wiley-Interscience, 1987.
Jacobinski H.: Genera and decompositions of lattices over orders,. Acta Math. 121, 1–29 (1968)
M.R. Gabel, Stably free projectives over commutative rings: PhD. Thesis, Brandeis University (1972).
T.Y. Lam, Serre’s problem on projective modules, Springer-Verlag (2006).
D.G. Quillen, Projective modules over polynomial rings, Invent. Math. 36 (1976), 167–171.
A.A. Suslin, Projective modules over polynomial rings are free, Soviet Dokl. Math. 17 (1976), 1160–1164.
R.G. Swan, K-Theory of finite groups and orders. (notes by E.G. Evans). Lecture Notes in Mathematics 149, Springer-Verlag 1970.
R.G. Swan, Projective modules over Laurent polynomial rings, Trans. Amer. Math. Soc. 237 (1978), 111–120.
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Johnson, F.E.A. Stably free cancellation for abelian group rings. Arch. Math. 102, 7–10 (2014). https://doi.org/10.1007/s00013-013-0599-8
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DOI: https://doi.org/10.1007/s00013-013-0599-8