Geodesic
Orbits of the group $\mathbf{GL}(r,k[X_1,\dots,X_n])$
Izvestiya. Mathematics , Tome 8 (1974) no. 3, pp. 490-500

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In this paper it is shown that the study of projective metabelian Lie algebras of finite rank reduces to a partial solution of Serre's problem on projective modules over polynomial rings. It is also observed that projective commutative-associative algebras of dimension 1 are isomorphic to the ring of polynomials in one variable over the ground field. 
@article{IM2_1974_8_3_a3,
     author = {V. A. Artamonov},
     title = {Orbits of the group $\mathbf{GL}(r,k[X_1,\dots,X_n])$},
     journal = {Izvestiya. Mathematics },
     pages = {490--500},
     publisher = {mathdoc},
     volume = {8},
     number = {3},
     year = {1974},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1974_8_3_a3/}
}
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V. A. Artamonov. Orbits of the group $\mathbf{GL}(r,k[X_1,\dots,X_n])$. Izvestiya. Mathematics , Tome 8 (1974) no. 3, pp. 490-500. http://geodesic.mathdoc.fr/item/IM2_1974_8_3_a3/