7 citations · 11 across the 11 of their papers we have counts for
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Vanishing of quaternionic cohomology groups and applications
Jasna Prezelj, Fabio Vlacci
We present solutions to additive and multiplicative Cousin problems formulated on an axially symmetric domain for slice--regular functions starting from the so…
Quaternionic Cartan coverings and applications
Jasna Prezelj, Fabio Vlacci
We present the topological foundations for the solvability of Multiplicative Cousin problems formulated on an axially symmetric domain In particular, we provi…
Resultants of slice regular polynomials in two quaternionic variables
Anna Gori, Giulia Sarfatti, Fabio Vlacci
We introduce a non-commutative resultant, for slice regular polynomials in two quaternionic variables, defined in terms of a suitable Dieudonné determinant.We use this tool to inve…
A Strong Version of the Hilbert Nullstellensatz for slice regular polynomials in several quaternionic variables
Anna Gori, Giulia Sarfatti, Fabio Vlacci
In this paper we prove a strong version of the Hilbert Nullstellensatz in the ring of slice regular polynomials in several quaternionic variables. Our p…
On a continuation of quaternionic and octonionic logarithm along curves and the winding number
Graziano Gentili, Jasna Prezelj, Fabio Vlacci
This paper focuses on the problem of finding a continuous extension of the hypercomplex logarithm along a path. While a branch of the complex logarithm can be defined in a small op…
Zero sets and Nullstellensatz type theorems for slice regular quaternionic polynomials
Anna Gori, Giulia Sarfatti, Fabio Vlacci
We study the vanishing sets of slice regular polynomials in several quaternionic variables. We obtain a geometric description of the vanishing sets in two variables, which leads to…
On a definition of logarithm of quaternionic functions
Graziano Gentili, Jasna Prezelj, Fabio Vlacci
For a slice--regular quaternionic function the classical exponential function is not slice--regular in general. An alternative definition of exponential function, the…
Slice conformality and Riemann manifolds on quaternions and octonions
Graziano Gentili, Jasna Prezelj, Fabio Vlacci
In this paper we establish quaternionic and octonionic analogs of the classical Riemann surfaces. The construction of these manifolds has nice peculiarities and the scrutiny of Ber…
On a class of automorphisms in which resemble the property of preserving volume
Jasna Prezelj, Fabio Vlacci
We give a possible extension for shears and overshears in the case of two non commutative (quaternionic) variables in relation with the associated vector fields and flows. We prese…