安徽大学学报（自然科学版）2024，Vol.48Issue(6)：30-36,7.DOI:10.3969/j.issn.1000-2162.2024.06.005
两类PI-代数的生成恒等式
Generating identities of two classes of PI-algebras
摘要
Abstract
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Key words
PI-algebra/T-ideal/Operad/truncation ideal/generating identities分类
数理科学引用本文复制引用
张远峰,徐江南,鲍炎红..两类PI-代数的生成恒等式[J].安徽大学学报（自然科学版）,2024,48(6):30-36,7.基金项目
国家自然科学基金面上项目(12371015) （12371015）
安徽省杰出青年基金项目(2108085J01) （2108085J01）
