摘要:

We classify pointed Hopf algebras of dimension 16 over an algebraically closed field of characteristic zero. Apart from the 11 group algebras, there are 29 such Hopf algebras. All of them can be obtained using the Ore extension construction, as described recently by Beattie, the second author, and Grunenfelder.

ISSN:0092-7872    

DOI:10.1080/00927870008826843

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

A complete description of isomorphisms between Ore extension Hopf algebras is given and used to enumerate all Ore extension Hopf algebrasHwith ∣G(H)∣ = 4 and skew-primitives whose square lies inH0.

ISSN:0092-7872    

DOI:10.1080/00927870008826844

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927870008826845

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927870008826846

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

Let υ be a prime divisor of a 2-dimensional regular local ring (Rm) with algebraically closed residue fieldk. Zariski showed that a prime divisor υ ofRis uniquely associated to a simplem-primary integrally closed idealIofR, there exist finitely many simple υ-ideals includingI, and all the other υ-ideals can be uniquely factored into products of simple υ-ideals. It is known that such anm-primary idealIofRcan be minimally generated by o(I) + 1 elements.Given a simple integrally closed idealIof order one with arbitrary rank and its associated prime divisor υ, we find minimal generating sets of all the simple υ-ideals and describe factorizations of all the composite υ-ideals in terms of power products of simple υideals as explicitly as possible.

ISSN:0092-7872    

DOI:10.1080/00927870008826847

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

We study the unitary subgroupV*(F2G) in the group algebras F2Gof 2-groups of maximal class over the field F2of two elements. We show that there does not exist a normal complement toGinV*(F2G) if and only ifGis the dihedral group of order 2n(n≥ 5) or the semidihedral group of order 2n(n≥5). We also describeV*(F2G) when the subgroupGhas order 8 and 16 and in this case there exist a normal complement ofGinV*(F2G).

ISSN:0092-7872    

DOI:10.1080/00927870008826848

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927870008826849

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

In the present paper we give new properties on the Peirce decomposition for principal train algebras and we study for first time the Peirce decomposition for plenary train algebras. Next, we show interesting and important open problems for train algebras. In particular, an old problem for genetic algebras is solved. Thus, we prove that every genetic algebra is plenary train algebra.

ISSN:0092-7872    

DOI:10.1080/00927870008826850

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927870008826851

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927870008826852

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor