3 citations · 17 across the 16 of their papers we have counts for
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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…
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…
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…
Picard-Vessiot Extensions of Real Differential Fields
Teresa Crespo, Zbigniew Hajto
For a linear differential equation defined over a formally real differential field K with real closed field of constants k, Crespo, Hajto and van der Put proved that there exists a…
Real and p-adic Picard-Vessiot fields
Teresa Crespo, Zbigniew Hajto, Marius van der Put
We consider differential modules over real and p-adic differential fields such that their field of constants is real closed (respectively p-adically closed). Using Deligne's work o…
Picard-Vessiot theory for real partial differential fields
Teresa Crespo, Zbigniew Hajto
We prove the existence of real Picard-Vessiot extensions for real partial differential fields with real closed field of constants. We establish a Galois correspondence theorem for…
Real Picard-Vessiot theory
Teresa Crespo, Zbigniew Hajto, Elzbieta Sowa
The existence of a Picard-Vessiot extension for a homogeneous linear differential equation has been established when the differential field over which the equation is defined has a…