摘要:

In this paper we show that ifB★His a bicrossproduct Hopf algebra then (B★H,R) is qusitriangular if and only ifRhas a unique decomposition:such thatQTVandUsatisfy certain compatible conditions. The result is applied to a certain bicrossproduct ofHandHop, whereHis a Hopf algebra with bijective antipode.

ISSN:0092-7872    

DOI:10.1080/00927870008827124

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

LetGbe a group and letKbe a field of characteristicp> 0. If all irreducible representations of the group algebraK[G] have finite degree < n, then we show thatGhas a subgroupAwith |G:A| bounded by a function ofnand such that all the irreducible representations ofK[A] have degree 1.

ISSN:0092-7872    

DOI:10.1080/00927870008827125

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927870008827126

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

In this paper we give some characterizations of a ringRwhose unique maximal nil ideal Nr(R) coincides with the set of all its nilpotent elements N(R) by using its minimal strongly prime ideals.

ISSN:0092-7872    

DOI:10.1080/00927870008827127

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

In the paper we investigate central polynomials for the matrix algebra with symplectic involution *. Their form is inspired by an approach of Formanek and Bergman for investigating matrix identities by means of commutative algebra. We find a necessary condition for the existence of central polynomials of the considered type and define their minimal degree. A description of such central polynomials forM4(K.*) is given. Some investigations are made forM6(K.*).

ISSN:0092-7872    

DOI:10.1080/00927870008827128

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

Consider the action of a finite groupGon a setM. Then the Galois number is defined to be 1 +f, wherefis the maximal number of fixed points of an element inG, which does not act as the identity onM. We determine the Galois number and the minimal degree of all doubly transitive permutation groups.

ISSN:0092-7872    

DOI:10.1080/00927870008827129

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

Let A = k[x1,…,xn] be the polynomial algebra over a fieldkof characteristic 0Ian ideal ofA, M = A/IandαHPIthe (affine) Hilbert polynomial ofM. By further exploring the algorithmic procedure given in [CLO'] for deriving the existence ofαHPI, we compute the leading coefficient ofαHPIby looking at the leading monomials of a Grobner basis ofIwithout computingαHPI. Using this result and the filtered-graded transfer of Grobner basis obtained in [LW] for (noncommutative) solvable polynomial algebras (in the sense of [K-RW]), we are able to compute the multiplicity of a cyclic module over the Weyl algebraAn(k) without computing the Hilbert polynomial of that module, and consequently to give a quite easy algorithmic characterization of the “smallest“ modules over Weyl algebras. Using the same methods as before, we also prove that the tensor product of two cyclic modules over the Weyl algebras has the multiplicity which is equal to the product of the multiplicities of both modules. The last result enables us to construct examples of “smallest“ irreducible modules over Weyl algebras.

ISSN:0092-7872    

DOI:10.1080/00927870008827130

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

Consider the blow upπ[Xtilde]→Xof a complex surfaceXat a point. Let Ẽ be a holomorphic bundle on [Xtilde]whose restriction to the exceptional divisor isO(j)n ⊗O(-j), and defineE+(π*E*)vv. Friedman and Morgan gave the following bounds for the second Chern classesj≤c2(Ẽ)-c2(E) ≤j2We show that these bounds are sharp.

ISSN:0092-7872    

DOI:10.1080/00927870008827131

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927870008827132

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

We study the classWof Hausdorff topological groupsGfor which the following two cardinal invariants coincide

ISSN:0092-7872    

DOI:10.1080/00927870008827133

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor