Among all $C^\infty$-algebras we characterize those which are algebras of $C^\infty$-functions on second countable Hausdorff $C^\infty$-manifolds.
@article{118859, author = {Peter W. Michor and Ji\v r\'\i\ Van\v zura}, title = {Characterizing algebras of $C^\infty$-functions on manifolds}, journal = {Commentationes Mathematicae Universitatis Carolinae}, volume = {37}, year = {1996}, pages = {519-521}, zbl = {0881.58001}, mrnumber = {1426917}, language = {en}, url = {http://dml.mathdoc.fr/item/118859} }
Michor, Peter W.; Vanžura, Jiří. Characterizing algebras of $C^\infty$-functions on manifolds. Commentationes Mathematicae Universitatis Carolinae, Tome 37 (1996) pp. 519-521. http://gdmltest.u-ga.fr/item/118859/
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