摘要:

Given (T,S,R), a Torsion-Torsion Free (T.T.F) theory in an abeiian category A with sufficient projective and injective objects. it is shown that the intersection of the full subcategories T and R is the additive category of fractions with respect to the Serre subcategory S, R ⋂ T is an abelian category. An equivalence is established between the subcategories of the projective objects of R ⋂ T and the projective objects of A in T. There is also a similar equivalence for injective objects. If T has a generating set of small projective objects, it is shown that R has a cogenerating set of indecomposable injectives.

ISSN:0092-7872    

DOI:10.1080/00927878808823609

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1988

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927878808823610

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1988

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927878808823611

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1988

数据来源: Taylor

摘要:

Iff= (In)n≥1 is filtration on a commutative ringRandEis anR-module, then a filtratione= (En)n≥1 onEis calledf-good in caseImIn⊂Em+nfor allm≥1 andn≥ 1 and there exists a positive integermsuch thatfor all n >m (This is an extension of the usual definition of e beingi-good withian ideal inR) A number of the basic results concerned withR-good filtrations are extended tof-good filtrations, and it is then shown that iff= (In)n≥1 andk= (Kn)n ≥1 are regular filtrations onRsuch thatKn⊆Infor all n ≥ 1, and ifkisf-good, then the complete integral closures of the Rees rings offandkare equal.

ISSN:0092-7872    

DOI:10.1080/00927878808823612

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1988

数据来源: Taylor

摘要:

An R-module M is said to be bounded if for any essential sub-module N of M, there exists an ideal K of R with K/ann(M) essential as a right ideal in R/ann(M) such that MK ⊆ N, The purpose of this paper is to provide conditions on a bounded module M that determine when R/ann(M) is right FBN.

ISSN:0092-7872    

DOI:10.1080/00927878808823613

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1988

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927878808823614

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1988

数据来源: Taylor

摘要:

Let A be a Mori domain; is it true that A[[XJ] is also a Mori domain? I give several instances where the answer is positive, even though I conjecture that there is a Mori domain A such that A[[X1] is not a Mori domain.

ISSN:0092-7872    

DOI:10.1080/00927878808823615

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1988

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927878808823616

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1988

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927878808823617

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1988

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927878808823618

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1988

数据来源: Taylor