| 摘要: |
| 本文研究了三角代数是否是零积决定的代数的问题.利用零积决定的代数的等价条件和代数方法,获得了三角代数是零积决定的代数的条件,推广了矩阵代数是零积决定的代数的结果.作为应用,得到零积决定的代数的零积导子一定是准导子. |
| 关键词: 三角代数 零积决定的代数 零积导子 准导子 |
| DOI： |
| 分类号:O151.21 |
| 基金项目:湖南省教育厅资助项目(05C694);怀化学院资助项目(HHUY2012-01). |
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| ZERO PRODUCT DETERMINED TRIANGULAR ALGEBRAS |
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XIE Le-ping1, WANG Deng-yin2
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1.Department of Mathematics, Huaihua College, Huaihua 418008, China;2.Department of Mathematics, China University of Mining and Technology, Xuzhou 221116, China
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| Abstract: |
| This paper researches by algebraic methods whether the triangular algebra is the zero (resp., Lie, Jordan) product determined algebra and obtains that △ is a zero (resp., Lie, Jordan) product determined algebra if A and B are zero (resp., Lie, Jordan) product determined algebras. It generalizes the results that matrix algebra is zero product determined algebra. Applying these we show that zero product derivations of △ are quasi-derivations. |
| Key words: triangular algebra zero product determined algebra zero product derivation quasi-derivation |
