摘要:

In this paper some conditions for a skew group ring or a crossed product to have finite weak global dimension are given.Using these results we obtain some necessary conditions and some sufficient conditions for a skew group ring or a crossed product to be a Dubrovin valuation ring.IfR*Gis a skew group ring, where the coefficient ringRis a commutative ring andGis a finite group, then we prove that the conditions we obtained become necessary and sufficient conditions.In particular, ifRis a commutative valuation ring, thenR*Gis a Dubrovin valuation ring if and only ifGT=<1>,whereGTis the inertial group ofR.

ISSN:0092-7872    

DOI:10.1080/00927879808826130

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1998

数据来源: Taylor

摘要:

IfC,Vare Grothendieck categories andF:C→D,G:D→Care functors satisfying convenient conditions, the extension an restriction of torsion theories preserves the compatibility.Moreover, two idempotent kernel functors are compatible inDif, and only if, their extensions are compatible inC.Finally, whenC,Dare symmetric closed, we obtain relations between exact sequences of Picard and Brauer groups for the extension and restriction of torsion theories.

ISSN:0092-7872    

DOI:10.1080/00927879808826131

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1998

数据来源: Taylor

摘要:

We show that theK0-group of a finite dimensional semisimple Hopf algebra has a natural structure of a ring with involution and prove that this ring is a twisting invariant of the Hopf algebra.We also study relations between algebraic structure of a Hopf algebra and the one of itsK0ring and prove that the twisting of a finite simple group is a simple Hopf algebra (i.e., it does not have proper normal Hopf subalgebras).In this case the dual Hopf algebra does not have proper Hopf subalgebras.Further, we construct several series of non trivial Hopf algebras by the twisting of the classical series of finite groups and give examples of Hopf algebras which can not be described as twisting of any group.

ISSN:0092-7872    

DOI:10.1080/00927879808826132

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1998

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879808826109

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1998

数据来源: Taylor