Hopf模代数与根理论(英文)

Hopf Module Algebras and Radical Theory

设H是一个Hopf代数,本文的目的是系统建立H—模代数的H—根理论。特别地,引入并研究了超幂零H—根、下H—根及特殊H—根,证明了Jacobson H—根是特殊H—根。本文可作为进一步研究Hopf模代数根理论的框架。

Let H be a Hopf algebra over a field. The objective of this paper is a systematic build up of a theory of H-radicals of H-module algebras. In particukr, the concepts of supernilpotent H-radicals, lower J-radical and special H-radicals are difined and investigated. It is shown that Jacobson H-radical is a special H-radical. The paper may serve also as a framework for further structural investigations of Hopf module algebras.