arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1806.02189math.OA
收藏

关联代数的广义Jordan导子

Generalized Jordan derivations of Incidence Algebras

Bruno Leonardo Macedo Ferreira, Tanise Carnieri Pierin, Ruth Nascimento Ferreira

备注：
7 pages. arXiv admin note: text overlap with arXiv:1411.6123 by other authors
阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

摘要：

对于给定的环$\mathfrak{R}$和局部有限预序集$(X, \leq)$，考虑$I(X, \mathfrak{R})$是$X$在$\mathfrak{R}$上的关联代数。受肖的一个结果的启发，即$I(X,\mathfrak{R})$的每个Jordan导子在$\mathfrak{R}$是$2$ -无挠的情况下都是一个导子，证明了$I(X,\mathfrak{R})$的每个广义Jordan导子在$\mathfrak{R}$是$2$ -无挠的的情况下都是一个广义导子，从而得到了上述结果.

英文摘要：

For a given ring $\mathfrak{R}$ and a locally finite pre-ordered set $(X, \leq)$, consider $I(X, \mathfrak{R})$ to be the incidence algebra of $X$ over $\mathfrak{R}$. Motivated by a Xiao's result which states that every Jordan derivation of $I(X,\mathfrak{R})$ is a derivation in the case $\mathfrak{R}$ is $2$-torsion free, one proves that each generalized Jordan derivation of $I(X,\mathfrak{R})$ is a generalized derivation provided $\mathfrak{R}$ is $2$-torsion free, getting as a consequence the above mentioned result.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

↑