On images of locally finite derivations and \(\mathcal{E}\)-derivations

DOI10.1016/j.jpaa.2018.07.002OpenAlexW2883595740MaRDI QIDQ1634853

Wenhua Zhao, A. R. P. van den Essen

Publication date: 18 December 2018

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1708.05813

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)

Related Items (6)

Image of linear K -derivations and linear ΚƐ-derivations of K [ x ₁ , x ₂ , x ₃ , x ₄ ] ⋮ Images of linear derivations and linear E-derivations of K[x,y,z] ⋮ Images of locally finite \(\mathcal{E} \)-derivations of bivariate polynomial algebras ⋮ Images of ideals under derivations and ℰ-derivations of univariate polynomial algebras over a field of characteristic zero ⋮ Unnamed Item ⋮ An ideal-theoretic approach to Keller maps

Cites Work

• Mathieu subspaces of associative algebras
• Images of locally finite derivations of polynomial algebras in two variables
• On the hypersurface \(x+x^2y+z^2+t^3=0\) in \(\mathbb{C}^4\) or a \(\mathbb{C}^3\)-like threefold which is not \(\mathbb{C}^3\)
• Constant terms in powers of a Laurent polynomial
• Polynomial automorphisms and the Jacobian conjecture
• Idempotents in intersection of the kernel and the image of locally finite derivations and \(\mathcal{E}\)-derivations
• A counterexample to the fourteenth problem of Hilbert in dimension four
• Generalizations of the image conjecture and the Mathieu conjecture
• The LNED and LFED conjectures for algebraic algebras
• On the cancellation problem for the affine space \(\mathbb{A}^{3}\) in characteristic \(p\)
• Some open problems on locally finite or locally nilpotent derivations and ℰ-derivations
• Quasi-translations and counterexamples to the Homogeneous Dependence Problem
• Introduction to Lie Algebras and Representation Theory
• Algebraic theory of locally nilpotent derivations
• Unnamed Item

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