Geodesic
Projective nonfree modules over group rings of solvable groups
Sbornik. Mathematics, Tome 44 (1983) no. 2, pp. 207-217 
V. A. Artamonov. Projective nonfree modules over group rings of solvable groups. Sbornik. Mathematics, Tome 44 (1983) no. 2, pp. 207-217. http://geodesic.mathdoc.fr/item/SM_1983_44_2_a4/
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     author = {V. A. Artamonov},
     title = {Projective nonfree modules over group rings of solvable groups},
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     volume = {44},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1983_44_2_a4/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

For a rather large class of commutative rings $k$ and locally solvable groups $G$ it is shown that there exist at least countably many nonisomorphic left ideals $P$ in the group algebra of $G$ such that $P\oplus kG\simeq kG+kG$. Bibliography: 12 titles.

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[4] Berridge P. H., Dunwoody M. J., “Non-free projective modules for torsion-free groups”, J. London Math. Soc., 19 (1979), 433–436 | DOI | MR | Zbl

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[7] Zalesskii A. E., Mikhalev A. V., “Gruppovye koltsa”, T. 2, Sovremennye problemy matematiki., VINITI, M., 1973, 5–118 | MR

[8] Neiman X., Mnogoobraziya grupp, Mir, M., 1969 | MR

[9] Lam V. T., “Serre's conjecture”, v. 635, Lecture Notes in Math., Springer-Verlag, Berlin, Heidelberg, New York, 1978

[10] Remeslennikov V. N., Sokolov V. G., “Nekotorye svoistva vlozhenii Magnusa”, Algebra i logika, 90 (1970), 566–578 | MR

[11] Serr Zh. P., Kurs arifmetiki, Mir, M., 1972 | MR | Zbl

[12] Burbaki N., Kommutativnaya algebra, Mir, M., 1971 | MR