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Rings of differential operators over rational affine curves

Gail Letzter; Leonid Makar-Limanov — 1990

Bulletin de la Société Mathématique de France

On the ring of constants for derivations of power series rings in two variables

Leonid Makar-Limanov; Andrzej Nowicki — 2001

Colloquium Mathematicae

Let k[[x,y]] be the formal power series ring in two variables over a field k of characteristic zero and let d be a nonzero derivation of k[[x,y]]. We prove that if Ker(d) ≠ k then Ker(d) = Ker(δ), where δ is a jacobian derivation of k[[x,y]]. Moreover, Ker(d) is of the form k[[h]] for some h ∈ k[[x,y]].

Degree estimate for subalgebras generated by two elements

Leonid Makar-Limanov; Jie-Tai Yu — 2008

Journal of the European Mathematical Society

We develop a new combinatorial method to deal with a degree estimate for subalgebras generated by two elements in different environments. We obtain a lower bound for the degree of the elements in two-generated subalgebras of a free associative algebra over a field of zero characteristic. We also reproduce a somewhat refined degree estimate of Shestakov and Umirbaev for the polynomial algebra, which plays an essential role in the recent celebrated solution of the Nagata conjecture and the strong...

$ℂ^{*}$ -actions on $ℂ^{3}$ are linearizable.

Kaliman, Shulim I.; Koras, Mariusz; Makar-Limanov, Leonid; Russell, Peter — 1997

Electronic Research Announcements of the American Mathematical Society [electronic only]

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