两类PI-代数的生成恒等式  

Generating identities of two classes of PI-algebras

作　　者：张远峰 徐江南 鲍炎红[1] ZHANG Yuanfeng;XU Jiangnan;BAO Yanhong(School of Mathematical Sciences,Anhui University,Hefei 230601,China)

机构地区：[1]安徽大学数学科学学院,安徽合肥230601

出　　处：《安徽大学学报（自然科学版）》2024年第6期30-36,共7页Journal of Anhui University(Natural Science Edition)

基　　金：国家自然科学基金面上项目(12371015);安徽省杰出青年基金项目(2108085J01)。

摘　　要：PI-代数所满足的恒等式构成自由代数的T-理想,是PI-代数研究的重要研究内容.经典的Kemer定理指出特征零域上的T-理想都可由有限多个多项式生成.但关于T-理想的生成多项式的计算是很困难的.基于自由代数的T-理想与含幺结合代数Operad的理想之间的对应关系,通过计算含幺结合代数Operad的截面理想分支的生成元,给出了具有2,3阶多项式增长余维数序列的含幺结合PI-代数的生成恒等式.The set of identities of a PI-algebra forms a T-ideal of free associative algebra,which is an important branch in the study of PI-algebra.The classical Kemer's theorem pointed out that a T-ideal can always be generated by finitely many polynomials if the base field is of characteristic zero.However,it is difficult to compute the generating polynomials for a T-ideal in general.Based on the correspondence between the T-ideal of the free algebra and the ideal of the unitary associative algebra operad,the generators of the components of truncation ideals of unitary associative algebra operad were calculated,and the generating identities of unitary associative PI-algebras with codimension sequences of polynomial growth of orders 2 and 3 were obtained.

关 键 词：PI-代数 T-理想 OPERAD 截面理想 生成恒等式 

分 类 号：O152.6[理学—数学]