AI 中文总结
本文研究半素结合代数的代数导子与相关自同构群的根性质，证明其素根与弱可解根重合，并联系Martindale商环内导子描述。
AI 中文摘要
本文延续了两条研究脉络：一是关于半素结合代数的代数导子可用其对称Martindale商环的内导子来描述的经典研究；二是利用与代数导子相关的代数自同构群这一实例，研究PI-环乘法群子群的素根与弱可解根重合的结果。
英文摘要
The paper "Algebraic derivations and radicals of automorphism groups of algebras" continues both the well-known line of description of algebraic derivations of semiprime associative algebras in terms of inner derivations of their symmetric Martindale rings of quotients, and results on the coincidence of the prime and weakly solvable radicals of subgroups of multiplicative groups of PI-rings using the example of automorphism groups of algebras associated with their algebraic derivations.
