论文标题
莱布尼兹代数的代数和类似于马丁代尔的商的代数
Algebras of quotients and Martindale-like quotients of Leibniz algebras
论文作者
论文摘要
在本文中，引入了代数的代数和类似于马达代尔的Qoutients的定义，并确定了两位商之间的相互作用。首先，研究了一些重要的特性，这些特性不仅适用于莱布尼兹代数，而且还可以将其解除到其代数的代数。其次，对于任何半弹药莱布尼兹代数，其最大代数的代数是构成的，并描述了最大代数的Passman样表征。第三，检查了相应的莱布尼兹代数的左右乘法算子生成的莱布尼兹代数与关联代数之间的关系。最后，引入了通过密集扩展的密集扩展和一些关于莱布尼亚代数的重要特性的定义。
In this paper, the definitions of algebras of quotients and Martandale-like qoutients of Leibniz algebras are introduced and the interactions between the two quotients are determined. Firstly, some important properties which not only hold for a Leibniz algebras but also can been lifted to its algebras of quotients are investigated. Secondly, for any semiprime Leibniz algebra, its maximal algebra of quotients is constucted and a Passman-like characterization of the maximal algebra is described. Thirdly, the relationship between a Leibniz algebra and the associative algebra which is generated by left and right multiplication operators of the corresponding Leibniz algebras of quotients are examined. Finally, the definition of dense extensions and some vital properties about Leibnia algebras via dense extensions are introduced.
