摘要:

Abstract. LetRbe a finite-dimensional central simpleC-algebra with involution * of the first kind, charR≠ 2 and letE*(R)be theC-subspace ofR, spanned by all projections. In this paper we prove a proposition concerning invariant submodules in prime rings with involution and then decideE*(R). As a consequence we prove the power reduction property for generalized identities of symmetric elements in a 2-torsion free semiprime ring with involution.

ISSN:0092-7872    

DOI:10.1080/00927879908826579

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

摘要:

In this paper, we examine the following question:do two conditions imply the third one in the '2 out of 3' Lemma (see e.g. Lemma 9.5 in [Alp86, p. 68])?We get a positive answer in two implications for p-nilpotent groups (Section 2) and give some counterexamples in case of soluble groups (see Section 3).

ISSN:0092-7872    

DOI:10.1080/00927879908826580

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

摘要:

LetKbe a field with charK≠ 3 and it two positive integers such that 1 ≤i<t/2,t≠ 3i. The classification problem for maximal Cohen-Macaulay modules overK[[X,Y]]/(Xt+Y3) is complicated ift≥ 6, because there exist parameter families of non-isomorphic maximal Cohen-Macaulay modules [Sc], or [GK], [Yo, Ch.9] and [DG]). Here we describe parameter families of such modulesN, such that N/YN is a direct sum of copies ofK[[X]]/(Xi)K[[X]]/(Xt-i).

ISSN:0092-7872    

DOI:10.1080/00927879908826581

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879908826582

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

摘要:

The (right)Ziegler spectrumof a ringRis a topological space the points of which are the isomorphism types of the indecomposablepure-injective(right)K-modules and is denoted byZgR. TheCB-rankof the Ziegler spectrum of a ringRis a measure for the complexity of the cat­egory ofK-modules. Them-dimensionof a module is a measure for the complexity of the lattice of itspp-definable subgroups. Using the clas­sification of the isomorphism types of the indecomposable pure-injective modules over a serial ring obtained by Eklof, Herzog and Puninski, weshow that if R is a serialring with Krull dimension, thenZgRhas CB-rank and for every point in ZgR, its CB-rank is equal to its m-dimension. We also show that a serial Krull-Schmidt ringRhas Krull dimension iff the largest theory of (right)R-modules hasm-dimension.

ISSN:0092-7872    

DOI:10.1080/00927879908826583

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

摘要:

We introduce a twisted higher rank generalization of generalized Weyl algebras and study simple weight modules over such algebras.

ISSN:0092-7872    

DOI:10.1080/00927879908826584

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

摘要:

In this paper, we obtain a recursive dimension formula for all γ- graded Lie algebras 𝔏 = +α∈γ𝔩αwith finite dimensional homogeneous sub-spaces, where T is a countable abelian semigroup satisfying a certain finiteness condition. We apply this dimension formula to several Lie algebras to obtain explicit and simple dimension formulas.

ISSN:0092-7872    

DOI:10.1080/00927879908826585

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879908826586

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

摘要:

LetDbe a commutative Dedekind domain,D, and let δ be a σ-derivation ofD, i.e.be an Ore extension, i.e. a ring generated byDandXsubject to the relations:. The aim of the paper is to classify the simpleA- modules (up to irreducible elements of certain Euclidean rings).

ISSN:0092-7872    

DOI:10.1080/00927879908826587

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

摘要:

Unital quadratic Jordan algebrasJ(q, I) determined by nondegenerate quadratic forms with basepoints over a field axe called full Jordan Clifford algebras. In characteristic 2 they have ample outer ideals which are also simple; they come in 3 sizes, tiny, small, and large, where the large are full Clifford algebras but the tiny and small algebras are lacking some of their parts. The simple algebras played a role in Zelmanov's solution of the Burnside Problem. In this paper we will analyze these in more detail, determining their centroids and their local algebras; this is important in the classification of prime Jordan triples of Clifford type in arbitrary char-acterstics. In addition we make a careful charcterization of the tiny, small, and large Clifford algebras. We use this to straighten one or two missteps in a proof from the classification of simple algebras. An important role in our characterization is played by commutators, and we describe the Jor­dan commutator products and Bergmann formulas for Clifford algebras in general.

ISSN:0092-7872    

DOI:10.1080/00927879908826588

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor