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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2022.10
- 수록면
- 957 - 967 (11page)
- DOI
- 10.4134/CKMS.c210346
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초록· 키워드
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Recently, Bre\v{s}ar's Jordan $\{g,h\}$-derivations have been investigated on triangular algebras. As a first aim of this paper, we extend this study to an interesting general context. Namely, we introduce the notion of Jordan $\mathcal{G}_n$-derivations, with $n \ge 2$, which is a natural generalization of Jordan $\{g,h\}$-derivations. Then, we study this notion on path algebras. We prove that, when $n > 2$, every Jordan $\mathcal{G}_n$-derivation on a path algebra is a $\{g,h\}$-derivation. However, when $n = 2$, we give an example showing that this implication does not hold true in general. So, we characterize when it holds. As a second aim, we give a positive answer to a variant of Lvov-Kaplansky conjecture on path algebras. Namely, we show that the set of values of a multi-linear polynomial on a path algebra $KE$ is either $\{0\}$, $KE$ or the space spanned by paths of a length greater than or equal to $1$.
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