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Haifeng Tian

Publications and source records attributed to Haifeng Tian.

2 recordsLinked to original sources
arXiv2023

Images of locally finite $\mathcal{E}$-derivations of bivariate polynomial algebras

This paper presents an $\mathcal{E}$-derivation analogue of a result on derivations due to van den Essen, Wright and Zhao. We prove that the image of a locally finite $K$-$\mathcal{E}$-derivation of polynomial algebras in two variables over a field $K$ of characteristic zero is a Mathieu-Zhao subspace. This result together with that of van den Essen, Wright and Zhao confirms the LFED conjecture in the case of polynomial algebras in two variables.

math.AC↗
arXiv2021

Images of Linear Derivations and Linear E-derivations of K[x 1 ,x 2 ,x 3 ]

Let K be a field of characteristic zero. We prove that images of a linear K-derivation and a linear K-E-derivation of the ring K[x 1 ,x 2 ,x 3 ] of polynomial in three variables over K are Mathieu-Zhao subspaces, which affirms the LFED conjecture for linear K-derivations and linear K-E-derivations of K[x 1 ,x 2 ,x 3 ].

math.AC↗