2 citations · 5 across the 11 of their papers we have counts for
12 papers
Order and Pascal depth of Pascal finite automorphisms of the plane
Elżbieta Adamus, Zbigniew Hajto
Let be a field of characteristic . For a Pascal finite automorphism of the affine plane we show that its order is determined by its Pascal depth, $|F|=p^{\lceil\log_pτ…
On the Jung-van der Kulk decomposition into Pascal finite factors
Elżbieta Adamus, Zbigniew Hajto
Combining the Jung--van der Kulk theorem with the conjugacy invariance of the Pascal finite class, we show that every polynomial automorphism of the plane over an arbitrary fie…
Strongly nilpotent automorphisms are Pascal finite
Elżbieta Adamus, Zbigniew Hajto
We compare two classes of polynomial automorphisms, strongly nilpotent and Pascal finite. We conclude that every strongly nilpotent automorphism is a Pascal finite one, but not vic…
A note on algorithmic approach to inverting multivariate formal power series
Elżbieta Adamus
In our previous paper an effective algorithm for inverting polynomial automorphisms was proposed. We extend its application to the case of formal power series over a field of arbit…
On the differential transcendentality of the Morita p-adic gamma function
Elżbieta Adamus
In this note we prove that for any given prime number the Morita -adic gamma function is differentially transcendental over .
Algorithm for studying polynomial maps and reductions modulo prime number
Elżbieta Adamus, Paweł Bogdan
In our previous paper an effective algorithm for inverting polynomial automorphisms was proposed. Also the class of Pascal finite polynomial automorphisms was introduced. Pascal fi…
Jacobian Conjecture via Differential Galois Theory
Elzbieta Adamus, Teresa Crespo, Zbigniew Hajto
We prove that a polynomial map is invertible if and only if some associated differential ring homomorphism is bijective. To this end, we use a theorem of Crespo and Hajto linking t…
On some nice polynomial automorphisms
Elzbieta Adamus, Pawel Bogdan, Teresa Crespo +1
Given a polynomial endomorphism F of the n-dimensional affine space over a field K, we define a sequence of polynomial endomorphisms of the affine space associated to F. We call F…
A new characterization of the invertibility of polynomial maps
Elzbieta Adamus, Pawel Bogdan, Teresa Crespo +1
In this paper we present an equivalent statement to the Jacobian conjecture. For a polynomial map F on an affine space of dimension n, we define recursively n finite sequences of p…
Jacobian Conjecture and Nilpotency
Elzbieta Adamus, Pawel Bogdan, Teresa Crespo +1
For K a field of characteristic 0 and d any integer number greater than or equal to 2, we prove the invertibility of polynomial endomorphisms of the affine space of dimension d ove…
An effective approach to Picard-Vessiot theory and the Jacobian Conjecture
Elzbieta Adamus, Pawel Bogdan, Zbigniew Hajto
In this paper we present a theorem concerning an equivalent statement of the Jacobian Conjecture in terms of Picard-Vessiot extensions. Our theorem completes the earlier work of T.…
An inversion algorithm for polynomial maps
Elzbieta Adamus, Pawel Bogdan, Teresa Crespo +1
We present an algorithmic equivalent statement to the Jacobian conjecture. Given a polynomial map F on an affine space of dimension n, our algorithm constructs n sequences of polyn…