【摘 要】
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Let H be a finite-dimensional pointed Hopf algebra of rank one over an algebraically closed field of characteristic zero.In this paper we show that any finite-dimensional indecomposable H-module is generated by one element.In particular,any indecomposable
【机 构】
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School of Mathematical Science,Yangzhou University Yangzhou,Jiangsu 225002,China;Department of Mathe
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Let H be a finite-dimensional pointed Hopf algebra of rank one over an algebraically closed field of characteristic zero.In this paper we show that any finite-dimensional indecomposable H-module is generated by one element.In particular,any indecomposable submodule of H under the adjoint action is generated by a special element of H.Using this result,we show that the Hopf algebra H is a principal ideal ring,i.e.,any two-sided ideal of H is generated by one element.As an application,we give explicitly the generators of ideals,primitive ideals,maximal ideals and completely prime ideals of the Taft algebras.
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