论文标题
某些可使用的代数的换向器理想的产品
Products of commutator ideals of some Lie-admissible algebras
论文作者
论文摘要
在本文中，我们主要研究了托管代数，例如诺维科夫代数，双公共代数和assosymmemetric代数的换向者理想。更确切地说，我们首先研究了Novikov代数和双公共代数的下部中央链的性质。然后，我们证明，对于每个谎言，nilpotent novikov代数或谎言nilpotent bicomutative代数$ \ Mathcal {a} $，是$ \ Mathcal {a} $的理想，由集合$ \ \ \ \ \ {ab -ba -ba \ ba \ mid a，b \ in \ in \ in \ int \ natercal a a a a ab -ba -ba -ba -ba -ba -b \ nilp最后，我们研究了下部中央链的特性，用于代数，研究助理代数的换向器理想的产物，并表明换向器理想的产物具有与联想代数相似的特性。
In this article, we mainly study the products of commutator ideals of Lie-admissible algebras such as Novikov algebras, bicommutative algebras, and assosymmetric algebras. More precisely, we first study the properties of the lower central chains for Novikov algebras and bicommutative algebras. Then we show that for every Lie nilpotent Novikov algebra or Lie nilpotent bicommutative algebra $\mathcal{A}$, the ideal of $\mathcal{A}$ generated by the set $\{ab - ba\mid a, b\in \mathcal{A}\}$ is nilpotent. Finally, we study properties of the lower central chains for assosymmetric algebras, study the products of commutator ideals of assosymmetric algebras and show that the products of commutator ideals have a similar property as that for associative algebras.
