Geodesic
Generalization of a theorem on the equivalence of the coordinate and algebraic definitions of a smooth manifold
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh Winter Mathematical School "Modern Methods of Function Theory and Related Problems." January 28 – February 2, 2019. Part 2, Tome 171 (2019), pp. 114-117.

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In this paper, we generalize the theorem on the equivalence of the coordinate and algebraic definitions of a smooth manifold. Within the framework of the algebraic approach, a point is considered as a homomorphism from the algebra of smooth real functions defined on a manifold into the field of real numbers. We consider a generalization for the case where the field of real numbers is replaced by an arbitrary associative normalized algebra, generally speaking, noncommutative.
Keywords: associative algebra, manifold, central algebra.
Mots-clés : homomorphism of algebras 
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     title = {Generalization of a theorem on the equivalence of the coordinate and algebraic definitions of a smooth manifold},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
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M. N. Krein. Generalization of a theorem on the equivalence of the coordinate and algebraic definitions of a smooth manifold. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh Winter Mathematical School "Modern Methods of Function Theory and Related Problems." January 28 – February 2, 2019. Part 2, Tome 171 (2019), pp. 114-117. http://geodesic.mathdoc.fr/item/INTO_2019_171_a9/

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