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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 저널정보
- 대한수학회 대한수학회보 대한수학회보 제59권 제1호
- 발행연도
- 2022.1
- 수록면
- 73 - 82 (10page)
- DOI
- 10.4134/BKMS.b210035
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초록· 키워드
오류제보하기
Let $K$ be a field of characteristic zero. We first show that images of the linear derivations and the linear $\mathcal{E}$-derivations of the polynomial algebra $K[x]=K[x_1,x_2,\ldots,x_n]$ are ideals if the products of any power of eigenvalues of the matrices according to the linear derivations and the linear $\mathcal{E}$-derivations are not unity. In addition, we prove that the images of $D$ and $\delta$ are Mathieu-Zhao spaces of the polynomial algebra $K[x]$ if $D=\sum_{i=1}^n(a_ix_i+b_i)\partial_i$ and $\delta=I-\phi$, $\phi(x_i)=\lambda_ix_i+\mu_i$ for $a_i,b_i,\lambda_i,\mu_i\in K$ for $1\leq i\leq n$. Finally, we prove that the image of an affine $\mathcal{E}$-derivation of the polynomial algebra $K[x_1,x_2]$ is a Mathieu-Zhao space of the polynomial algebra $K[x_1,x_2]$. Hence we give an affirmative answer to the LFED Conjecture for the affine $\mathcal{E}$-derivations of the polynomial algebra $K[x_1,x_2]$.
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