ISSN:0092-7872    

DOI:10.1080/00927870008826975

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

LetRbe a Marot ring whose regular ideals are finitely generated andDa Krull overring ofR. In this paper, we show that if reg-dimR≥ 2, then each regular ideal ofDis finitely generated and reg-dimD≥ 2. In particular, each regular ideal of a Krull overring of a Noetherijan ringRis finitely generated provided that (regular) Krull-dimensionR≥ 2. This is a generalization of the well-known fact that a Krull overring of a Noetherian domain with Krull-dimension ≥ 2 is also a Noetherian domain with Krull-dimension ≥ 2.

ISSN:0092-7872    

DOI:10.1080/00927870008826976

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

LetRbe a Krull domain with finite divisor class group Cl(R).We coinsider possible values of ρ(R), the elasticity of factorizations ofR. We first determine an upper bound on ρ(R) based on the distribution of height-one prime ideals in Cl(R) and characterize when his upper bound is attained. We concentrate on the case, wherepis a prime, and determine further bounds on ρ(R) whenk=1 (i.e., Cl(R= Zp). Unlike a related analysis for the cross number of Zpk, we show that the elasticities of such domains do not take on a complete set of hypothesized values.

ISSN:0092-7872    

DOI:10.1080/00927870008826977

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927870008826978

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927870008826979

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

LetRbea commutative ring with identity. AnR-module (ideal ofR)Ais called amultiplication module (ideal)if for each submoduleNofAthere exists an idealIofRwithN=I A. We give several characterizations of multiplication modules. Using the method of idealization we show how to reduce questions concerning multiplication modules to multiplication ideals. For example, we show that ifSis a commutative R-algebra and ψ:M→anR-module homomorphism whereMis a multiplicationR-module andNis anS-module, thenSψ(M) is a multiplicationS-module.

ISSN:0092-7872    

DOI:10.1080/00927870008826980

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

If G is a categorical group, a G-module is defined to be a braided categorical group (Ac) together with an action of G on (A,c). In this work we define the notions of singular extension of G by the G-module (A,c) and of 1-cocycle of G with coefficients in (A,c) and we obtain, first, a bijection between the set of equivalence classes of singular extensions of G by (Ac) and the set of equivalence classes of 1-cocycles. Next, we associate to any G-module (Ac) a Kan fibration of simplicial sets ϕ:Ner(GAc)) →Ner(G)and then we show that there is a bijection between the set of equivalence classes of singular extensions of G by (A,c) and Γ[Ner(G,A,c/Ner(G)]the set of fibre homotopy classes of cross-sections of the fibration ϕ.

ISSN:0092-7872    

DOI:10.1080/00927870008826981

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

The operatorshnandinand their dualshmacr;nandimacr;ndefined on the free semigroupX+for a nonempty setXby Gerhard and Petrich are proved here to be homomorphisms of onto certain subsets ofX+with a suitable multiplication. From the work of the authors mentioned, these operators induce fully invariant congruences onX+corresponding to join irreducible varieties of bands ifXis countably infinite. New operators onX+are defined by means of these operators which give homomorphisms in an analogous way and induce fully invariant congruences onX+corresponding to all varieties of bands except for the variety of all bands, and some varieties of normal bands. The former of these was investigated by the mentioned authors and the latter must be treated differently. By means of the above operators we are able to characterize all cases of relatively free bands.

ISSN:0092-7872    

DOI:10.1080/00927870008826982

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927870008826983

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927870008826954

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor