11 citations · 62 across the 33 of their papers we have counts for
38 papers
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…
Unfoldings of maps, the first results on stable maps, and results of Mather-Yau/Gaffney-Hauser type in arbitrary characteristic
Dmitry Kerner
Consider the (formal/analytic/algebraic) map-germs Maps(X,(k^p,o)). Let G be the group of right/contact/left-right transformations. I extend the following (classical) results from…
Orbits of the left-right equivalence of maps in arbitrary characteristic
Dmitry Kerner
The germs of maps (k^n,o)\to(k^p,o) are traditionally studied up to the right, left-right or contact equivalence. Various questions about the group-orbits are reduced to their tang…
Some genericity results over Noetherian rings
Dmitry Kerner
Let M be a filtered module. Some properties of elements of M are "generic" in the following sense: (being open/stable) if an element z of M has a property P then any approximation…
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,…