On the Image Conjecture for Locally Finite Derivations and $\mathcal E$-Derivations

DOI10.1016/J.JPAA.2018.07.002arXiv1708.05813MaRDI QIDQ6290268

Arno van den Essen, Wenhua Zhao

Publication date: 19 August 2017

Abstract: Some cases of the LFED Conjecture, proposed by the second author [Z3], for certain integral domains are proved. In particular, the LFED Conjecture is completely established for the field of fractions $k(x)$ of the polynomial algebra $k[x]$, the formal power series algebra $k[[x]]$ and the Laurent formal power series algebra $k[[x]][x^{-1}]$, where $x=(x_1,x_2,dots,x_n)$ denotes $n$ commutative free variables and $k$ a field of characteristic zero. Furthermore, the relation between the LFED Conjecture and the Duistermaat-van der Kallen Theorem [DK] is also discussed and emphasized.

Mathematics Subject Classification ID

Commutators, derivations, elementary operators, etc. (47B47) Derivations, actions of Lie algebras (16W25) Automorphisms and endomorphisms of algebraic structures (08A35) Modules, bimodules and ideals in associative algebras (16D99)

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