Geodesic
Projective nonfree modules over group rings of solvable groups
Sbornik. Mathematics, Tome 44 (1983) no. 2, pp. 207-217

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. 
@article{SM_1983_44_2_a4,
     author = {V. A. Artamonov},
     title = {Projective nonfree modules over group rings of solvable groups},
     journal = {Sbornik. Mathematics},
     pages = {207--217},
     publisher = {mathdoc},
     volume = {44},
     number = {2},
     year = {1983},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1983_44_2_a4/}
}
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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/