摘要:

A fundamental approach to the homological algebra of rational modules in positive characteristicpshould begin with the translation properties of injective modules. This point of view leads to the study of functors related to coherent translation and their effect on the injective indecomposable modules indexed byp-regular dominant weights. The main result shows that the calculation can often be reduced to a corresponding calculation on the principal indecomposable modules of the Frobenius kernel.1

ISSN:0092-7872    

DOI:10.1080/00927870008826824

出版商:Marcel Dekker, Inc.    

年代:2000

数据来源: Taylor

摘要:

Letbe an affine algebra over a fieldkof characteristic 0, and letbe the standard filtration onA. Consider the graded algebras associated with, the associated graded algebra ofA, and, the Rees algebra ofA. It is proved thatAis a solvable polynomial algebra within the sense of [K-RW] if and only ifG(A) is a solvable polynomial algebra withif and only ifis a solvable polynomial algebra withSuppose thatAis a solvable polynomial algebra with, LetLbe a left ideal ofAand. It is proved thatFis a (left) Groebner basis forLin the sense of [K-RW] if and only if, is a (left) Groebner basis forG(L) inG(A) if and only ifis a (left) Groebner basis for, whereG(L) resp.is the associated graded left ideal ofLinG(A) resp. the associated graded left ideal ofLinwith respect to the filtrationFLinduced byFAonL, and theresp.are corresponding homogeneous elements of theinG(L) resp. in. Examples of applications of this filtered-graded transfer method to some popular algebras are given.

ISSN:0092-7872    

DOI:10.1080/00927870008826825

出版商:Marcel Dekker, Inc.    

年代:2000

数据来源: Taylor

摘要:

Those linearly compact rings with identity having a simple group of units and a transfinitely nilpotent Jacobson radical are identified. A consequence of this characterization is Cohen and Koh's classification theorem for compact rings with identity having a simple group of units.

ISSN:0092-7872    

DOI:10.1080/00927870008826826

出版商:Marcel Dekker, Inc.    

年代:2000

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927870008826827

出版商:Marcel Dekker, Inc.    

年代:2000

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927870008826828

出版商:Marcel Dekker, Inc.    

年代:2000

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927870008826829

出版商:Marcel Dekker, Inc.    

年代:2000

数据来源: Taylor

摘要:

We study lattice-ordered groups whose set of branch points in the root system of regular subgroups satisfies descending chain condition. We show that these lattice-ordered groups fornl a torsion class. We also show that the class of finite-valued lattice-ordered groups that are also inis closed with respect to lattice-ordered subgroups, and such class has a unique archimedean closure.

ISSN:0092-7872    

DOI:10.1080/00927870008826830

出版商:Marcel Dekker, Inc.    

年代:2000

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927870008826831

出版商:Marcel Dekker, Inc.    

年代:2000

数据来源: Taylor

摘要:

We determine the structure of ap-pure[pure] hull of ap-purifiable [purifiable] subgroup of an arbitrary abelian group. Moreover, we prove that a subgroupAof an abelian groupGis purifiable inGif and only ifAisp-purifiable inGfor every primep. Using these results, we characterize the groupsGfor which all subgroups are purifiable inG. Furthermore, we establish several properties of purifiable subgroups.

ISSN:0092-7872    

DOI:10.1080/00927870008826832

出版商:Marcel Dekker, Inc.    

年代:2000

数据来源: Taylor

摘要:

LetAbe an artin algebra. An indecomposableA-moduleMis called weakly directing if it does not belong to a cycleof nonzero nonisomorphisms between indecomposable modules from the same component of. This paper deals with weakly directing modules. We investigate the distinctions and connections between weakly directing modules and directing modules. We also show that all weakly directing modules are distributed to finitely many DTr-orbits.

ISSN:0092-7872    

DOI:10.1080/00927870008826833

出版商:Marcel Dekker, Inc.    

年代:2000

数据来源: Taylor