摘要:

In order to obtain radicals of a Г-ring determined by strong nilpotency, nilpotency, and strongly nil property, we introduce a general method. Let P be an arbitrary property of Γ-rings. For any Γ-ring we construct a quasi-P radical determined by P. If P is homomorphically closed, then this quasi-P radical can be constructed by transfinite induction. We next study the relations of radicals among the quasi-strongly nil radical and other radicals of Г-rings. In view of these relations, we see that the quasi-strongly nil radical is a new radical in the radical theory of Г-rings.

ISSN:0092-7872    

DOI:10.1080/00927879908826429

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879908826430

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879908826431

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879908826432

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

摘要:

A technical lemma is proved for certain semigroups of matrices. It has several applications to problems concerning irreducible semigroups satisfying spectral conditions, e.g., submultiplicativity of spectrum. It is also used to give extensions of the following theorem of Brauer's. IfUis a finite group of complex matrices, so that for some integerm, everyUinU, satistiesUm=IthenUhas a representation over the cyclotomic fieldQ(ω), where ω is a primitivem-th root of unity.

ISSN:0092-7872    

DOI:10.1080/00927879908826433

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

摘要:

It is a well-known fact that ifKis a field, then the Hilbert series of a quotient of the polynomial ringby a homogeneous ideal is of the formwe call the polynomialq(t)the Hilbert numerator of the quotient algebra.

ISSN:0092-7872    

DOI:10.1080/00927879908826434

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

摘要:

LetKbe an algebraic function field with field of constantskand leiCbe the intersection of all but one of the valuation rings which determine the places ofK. This paper is concerned with the Serre groupsGL2(C). (Serre devotes much of his book “Trees” to their study.) Whenkis finiteCis an arithmetic Dedekind domain and (consequently) most of the work in this case has centred on the congruence subgroups. The purpose of this paper is to extend some of these results to the infinite case. Whenkis infinite it is proved, in particular, that, for infinitely manyC-idealsq, the principal congruence subgroupSL2(C, q), modulo its subgroup generated by unipotent matrices, has a free quotient of infinite rank. This result is used to extend known results on congruence hulls.

ISSN:0092-7872    

DOI:10.1080/00927879908826435

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879908826436

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

摘要:

In this paper we extend the study of the prime ideal structure of group rings initiated by Gilmer (1974), Brewer-Costa-Lady (1975), and Anderson-Bouvier-Dobbs-Fontana-Kabbaj (1988). Of particular inter-est is the transfer fromAtoA[G] of certain properties which are linked to the prime spectrum such asS-domain or Jaffard domain. Their study will follow the same lines as the usual approach to the study of prime ideal structure in polynomial rings.

ISSN:0092-7872    

DOI:10.1080/00927879908826437

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879908826438

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor