an:04017657
Zbl 0626.46057
Ogneva, O. S.
Coincidence of the homological dimensions of the Fr??chet algebra of smooth functions on a manifold with the dimension of the manifold
EN
Funct. Anal. Appl. 20, 248-250 (1986); translation from Funkts. Anal. Prilozh. 20, No. 3, 92-93 (1986).
00153336
1986
j
46M20 46H05 46J05
cohomological dimensions
The principal result of this paper is the following: ds \(C^{\infty}(M)=dg C^{\infty}(M)=db C^{\infty}(M)=m\); here M is a smooth real m-dimensional manifold, \(C^{\infty}(M)\) is the topological algebra of \(C^{\infty}\) functions on M and ds A, dg A, db A denote the cohomological dimensions of a topological algebra A in the sense of \textit{A. Ya. Khelemskij} [Homology in Banach and topological algebras (in Russian) (1986; Zbl 0608.46046)].
L.Maxim R??ileanu
Zbl 0608.46046