58 citations · 133 across the 18 of their papers we have counts for
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When does a derivation of a ring admit the exponential?
Genrich Belitskii, Alberto F. Boix, Dmitry Kerner
Exponentials of (real/complex) vector fields are classically defined via the vector field integration. Take a k-algebra k[x] \subset R\subset k[[x]], where k\supseteq \Q is a local…
Surjectivity of the completion map for rings of -functions. (Whitney extension theorem for general filtrations)
Genrich Belitskii, Dmitry Kerner
The classical lemma of Borel reads: any power series with real coefficients is the Taylor series of a smooth function. Algebraically this means the surjectivity of the completion m…
Approximation results of Artin-Tougeron-type for general filtrations and for -equations
Genrich Belitskii, Alberto F. Boix, Dmitry Kerner
Artin approximation and other related approximation results are used in various areas. The traditional formulation of such results is restricted to filtrations by powers of ideals,…
A strong version of implicit function theorem
Genrich Belitskii, Dmitry Kerner
We suggest the necessary/sufficient criteria for the existence of a (order-by-order) solution y(x) of a functional equation F(x,y)=0 over a ring. In full generality, the criteria h…