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On the hypersurfacex+x2y+z2+t3=0 in ℂ4 or a ℂ4-like threefold which is not C3
In this note it will be proved that the threefold in ℂ4 which is given byx+x2y+z2+t3=0 is not isomorphic to ℂ3. Here ℂ is the field of complex numbers.
Solution of Dirichlet's problem for the equation Δu =−1 in a convex region
Let u be a solution of the following boundary-value problem: u¦Γ = 0, where Γ is a closed convex curve and Δu = −1 in the region D bounded by Γ. Then u has only one local maximum, and all its levelExpand
Affine surfaces with AK(S)=C
Abstract. In this paper we give a description of hypersurfaces with AK(S) = C.Let X be an affine variety and let G(X) be the group generated by all C + -actions onX. Then AK(X) ⊂ O(X) is the subring ofExpand
On groups of automorphisms of a class of surfaces
In this note we describe the group of automorphisms of a commutative algebra with three generatorsx, y andz satisfying a relationxy= P(z), whereP(z) is a polynomial.
Algebraically closed skew fields
A conjecture of Bavula on homomorphisms of the Weyl algebras
Bavula states [V. Bavula, The inversion formulae for automorphisms of polynomial algebras and rings of differential operators in prime characteristic, J. Pure Appl. Algebra 212 (2008), pp. 2320–2337]Expand
On automorphisms of Weyl algebra
— In this note I am going to generalize a theorem of J. Dixmier [1] describing the group of automorphisms of the Weyl algebra to the case of non-zero characteristic and give a new proof of it in theExpand
The Freiheitssatz for Poisson algebras
Abstract We prove the Freiheitssatz for Poisson algebras in characteristic zero. We also give a new proof of the tameness of automorphisms for two generated free Poisson algebras and show that anExpand
On the Newton Polygon of a Jacobian Mate
This note contains an up-to-date description of the “minimal” Newton polygons of the polynomials satisfying the Jacobian condition.