ISSN:0092-7872    

DOI:10.1080/00927879808826316

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1998

数据来源: Taylor

摘要:

It is known that ifRis a right noetherian ring, then the corresponding Malcev-Neumann ringR* ((G)) is right noetherian and r.K.dim(R) = r.K.dim(R* ((G))). We prove that the right noethe-rianness is a necessary condition for a Malcev-Neumann ring to have right Krull dimension. Also, we consider uniform dimension of Malcev-Neumann rings. The results obtained are applied to some other ring constructions

ISSN:0092-7872    

DOI:10.1080/00927879808826317

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1998

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879808826318

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1998

数据来源: Taylor

摘要:

In [Gd] Goodearl proved that if for every essential submoduleNof a moduleMM/Nis a Noetherian module, then the moduleM/SocMis Noetherian. Then in [AS], Al-Khazzi and Smith got that if every small submodule of a module M is Artinian then so is the Jacobson radical 𝔍(M) ofM. These results are dual to each other in the lattice theory sense ( recall thatis essential submodule ofM}). However the proofs in [AS] and [Gd] are not dual at all. Hence it is natural to ask whether there is a common proof of the both results. The best it would be to extend one of these results to complete modular lattices or to a satisfactory subclass of such lattices. Then to get any of the results it would be enough to take the lattice of submodules of a module or its dual. Attempts to find such an extension inspired our studies in this paper. We did not settle the general problem but obtained such an extension in cases of complete modular lattices which are upper continuous, lower continuous or distributive. Moreover we got some general results on complete modular lattices which, applied to modules, give uniform proofs of several known results on dimensions of modules

ISSN:0092-7872    

DOI:10.1080/00927879808826319

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1998

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879808826320

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1998

数据来源: Taylor

摘要:

Abstract. LetGbe a nilpotent group. We prove that ifGsatisfies a certain per-mutational property on commutators of weight 4 then its 2-generator subgroups are metabelian

ISSN:0092-7872    

DOI:10.1080/00927879808826321

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1998

数据来源: Taylor

摘要:

We define Unipn(F2) to be the group of invertible upper-triangular matrices over F2, the field of 2 elements. Letsifori= 1,2,…,n- 1 denote the matrix whosne diagonal entries are all 1, and whose only other nonzero entry is in the ith row and (i+ 1)st column. Then it is easy to see that thesigenerate Unipn(F2). Reiner [4] gave relations among thesi, which he conjectured gave a presentation for Unipn(F2). We show that a subset of these relations suffice to present the group

ISSN:0092-7872    

DOI:10.1080/00927879808826322

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1998

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879808826323

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1998

数据来源: Taylor

摘要:

We develop a Goldie theory for associative pairs and characterize associative pairs which are orders in semiprime associative pairs coinciding with their socle, and those which are orders in semiprime artinian associative pairs

ISSN:0092-7872    

DOI:10.1080/00927879808826324

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1998

数据来源: Taylor

摘要:

We prove that a Priifer domainRhas an m-canonical idealJ, that is, an idealIsuch thatJ: (I:J) =Jfor every idealJofR, if and only ifRish-local with only finitely many maximal ideals that are not finitely generated; moreover, if these conditions are satisfied, then the product of the non-finitely generated maximal ideals is an m-canonical ideal ofR

ISSN:0092-7872    

DOI:10.1080/00927879808826325

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1998

数据来源: Taylor