摘要:

In [14] we established a relationship between genus and localization of finitely generated torsion-free abelian by finite groups aud grnus and localization integral representation theory. In this paper we strrcly the consequences of this relationship. We prove results about the genus of groups which are analogues to results in integral representaion theory. In particular we prove non-cancellation phenomena for finitely generated groups with finite commutator subgroups.

ISSN:0092-7872    

DOI:10.1080/00927870008827032

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

In this paper we study several structural properties of the monoidsPOPInof all injective orientation preserving partial transformations on a chain with n elements: we establish descriptions for the ideals and for the congruences of these monoids and we show thatPOPInis a 2-generated semigroup, for alln∈ N. Our main aim is to give a presentation for these monoids.

ISSN:0092-7872    

DOI:10.1080/00927870008827033

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

LetRbe a ring with identity and letbe a finite direct sum of relatively protectiveR-modulesMiThen it is proved thatMis lifting if and only ifMis amply supplemented andMiis lifting for all 1 ≤i≤n.Letbe a finite direct sum ofR-modulesMi. We prove thatMis (quasi-) discrete if and only ifare relatively projective (quasi-) discrete modules. We also prove that, for an amply supplementedR-moduleM=M1⊕M2such thatM1andM2have the finite exchange propertyMis lifting if and only ifM1andM2are lifting and relatively small projectiveR-modules and every co-closed submoduleNofMwithM=N+M1=N+M2is a direct summand ofM.Finally, we prove that, for a ringRsuch that every direct sum of a liftingR-module and a simpleR-module is lifting, every simpleR-module is smallM-projective for any liftingR-moduleM.

ISSN:0092-7872    

DOI:10.1080/00927870008827034

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

The aim of this paper is to introduce a notion of quantum groupoid, non-commutative analogue of Lie groupoids. This notion generalizes simultaneously the notion of a Hopf bigebroid [Mal] (corresponding to a quantum groupoid with commutative space of units) and the notion of a braided quantum group of Majid [Maj]. The commutativity hypothesis of the base in [Mal] is no more necessary and a construction of L. Vainerman [V] enters in this frame.

ISSN:0092-7872    

DOI:10.1080/00927870008827035

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927870008827036

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

LetBandHbe Hopf algebras of the same finite dimensionnSkew dual bases ofBandHare introduced and used to construct a quasitrian-gular structure of Doi-Takeuchi’s Hopf algebraB⋈TH. As the special cases, the quasitriangular structure of Drinfeld's doubleD(H) is obtained.

ISSN:0092-7872    

DOI:10.1080/00927870008827037

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

Letkbe an algebraically closed uncountable field of characteristic 0,ga finite dimensional solvablek-Lie algebraRa noetheriank-algebra on whichgacts byk-derivationsU(g) the enveloping algebra ofg,A=R*gthe crossed product ofRbyU(g)Pa prime ideal ofAand Ω(P) the clique ofP. Suppose that the prime ideals of the polynomial ringR[x] are completely prime. IfRisg-hypernormal, then Ω(P) is classical. Denote byATthe localised ring and letMbe a primitive ideal ofATSetQ=P∩RIn this note, we show that ifRis a strongly (R,g)-admissible integral domain and ifQRQis generated by a regularg-centralising set of elements, then

ISSN:0092-7872    

DOI:10.1080/00927870008827038

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927870008827011

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor