摘要:

It is well known that a group is free if and only if it acts freely without inversions on a tree. We prove a generalisation of this fact by defining a quasi-tree to be a graph with a bound on the size of its simple loops. It is shown that a finitely generated group acting freely on such a graph is isomorphic to a free product of free groups and finite groups.

ISSN:0092-7872    

DOI:10.1080/00927870008826873

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

All prime ideals of the enveloping algebraU=U(sl3), over an arbitrary field of characteristic zero, are listed by generators and classified by height. The inclusions between these ideals are also determined. Each prime idealIofUis presented by generators in several different ways. At one pole, we give a generating set forIas an adjoint module, and this includes a description for the expression of every possible highest weight element ofI. At the other pole, except for the case when the ideal is generated by the central variablesIhas a single generator as a two-sided ideal ofU.

ISSN:0092-7872    

DOI:10.1080/00927870008826874

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

We compute the coradical filtration and the group of Hopf algebra automorphisms of the non-restricted specialization of the quantized universal enveloping algebra of a finite-dimensional semisimple Lie algebra.

ISSN:0092-7872    

DOI:10.1080/00927870008826875

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

IfAis a Banach algebra andDis a Lie derivation onAsuch that for a fixedis in the radical ofAfor all a ∈ A, then [D(A)A] is contained in the radical ofA.

ISSN:0092-7872    

DOI:10.1080/00927870008826876

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927870008826877

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

An idealIin a commutative ringRis called az°-ideal ifIconsists of zero-divisors and for eacha∈Ithe intersection of all minimal prime ideals containingais contained inI.We prove that in a large class of rings, containing Noetherian reduced rings, Zero-dimensional rings, polynomials over reduced rings andC(X), every ideal consisting of zero-divisors is contained in a primez°-ideal. It is also shown that the classical ring of quotients of a reduced ring is regular if and only if every primez°-ideal is a minimal prime ideal and the annihilator of a f.g. ideal consisting of zero-divisors is nonzero. We observe thatz°-ideals behave nicely under contractions and extensions.

ISSN:0092-7872    

DOI:10.1080/00927870008826878

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

This article deals with the global dimension of rings of functions. An improved lower bound for global dimension is proved for von Neumann regular rings. IfXis a compact, Hausdorff and zero-dimensional space, and its weight and independence character coincide, then the global dimension of 𝔅(X), its Stone dual, can be calculated. The spaces for which these invariants agree are studied. Finally, it is shown that, except forP-spaces, the global dimension ofC(X) is at least 3.

ISSN:0092-7872    

DOI:10.1080/00927870008826879

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

LetAbe an Archimedean uniformly completef-algebra with unit element. It is proved that the following conditions are equivalent:(1)Ais semi-hereditary; (2)Ais coherent; (3)Ais projectable; (4)Ais Dedekind σ-complete.

ISSN:0092-7872    

DOI:10.1080/00927870008826880

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927870008826842

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor