摘要:

Central internal algebras are generalizations of Boolean rings and semilattices. We describe all ring and semigroup varieties consisting of central internal algebras.

ISSN:0092-7872    

DOI:10.1080/00927879908826668

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879908826669

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879908826670

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

摘要:

We prove that if an extensionR⊆Tof commutative rings satisfies the going-up property (for instance, ifTis an integral extension ofR), then any increasing chain of prime ideals ofR(indexed by an arbitrary linearly ordered set) is covered by some corresponding chain of prime ideals ofT. As a corollary, we recover the recent result of Kang and Oh that any such chain of prime ideals of an integral domainDis covered by a corresponding chain in some valuation overring ofD.

ISSN:0092-7872    

DOI:10.1080/00927879908826671

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879908826672

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879908826673

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

摘要:

LetRbe a left artinian ring such that every finitely presented right .ft-module is of finite endolength. It is shown that the cardinality of the set of isomorphism classes of preinjective rightR-modules is less than or equal to the cardinality of the set of isomorphism classes of preprojective leftR-modules, andRis of finite representation type if and only if these cardinal numbers are finite and equal to each other. As a consequence, we deduce a theorem, due to Herzog [17], asserting that a left pure semisimple ringRis of finite representation type if and only if the number of non-isomorphic preinjective rightR-modules is the same as the number of non-isomorphic preprojective left .R-modules. Further applications are also given to provide new criteria for artinian rings with self-duality and artinian Pi-rings to be of finite representation type, which imply in particular the validity of the pure semisimple conjecture for these classes of rings.

ISSN:0092-7872    

DOI:10.1080/00927879908826674

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

摘要:

LetIbe an ideal of the commutative ringRand letdenote the category ofR-modules andbe the subcategory of Noetherian (resp. Artinian)R-modules. LetNdenote a NoetherianR-module andN' be a submodule ofN. For a linear exact covariant (resp. contravriant) functoris determined and as a consequence several results concerning asymptotic prime ideals are deduced. For example, it is shown that both sequences of setsare eventually constant for largen. Also, the dual results are shown to be true for a linear exact functor.

ISSN:0092-7872    

DOI:10.1080/00927879908826675

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

摘要:

Given a ringR, consider the condition: (*) every maximal right ideal ofRcontains a maximal ideal ofR. We show that, for a ringRand 0 ≠e2=e∈Rsuch thatele⫋eReevery proper idealIofRRsatisfies (*) if and only if eRe satisfies (*). Hence with the help of some other results, (*) is a Morita invariant property. For a simple ringRR[x] satisfies (*) if and only ifR[x] is not right primitive. By this result, ifRis a division ring andR[x] satisfies (*), then the Jacobson conjecture holds. We also show that for a finite centralizing extensionSof a ringRRsatisfies (*) if and only ifSsatisfies (*).

ISSN:0092-7872    

DOI:10.1080/00927879908826676

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

摘要:

We study the structure of imaginary Verma modules induced from the"natural"Borel subalgebra of a toroidal Lie algebra. In particular, we establish a criterion of irreducibility for imaginary Verma modules and describe their submodules and irreducible quotients. We also describe the structure of Verma type modules in the case ofsl(2)-toroidal Lie algebra over two variables.

ISSN:0092-7872    

DOI:10.1080/00927879908826677

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor