摘要:

For a given ringR, letQr(R) (resp.Ql(R)) denote the maximal right (resp. left) quotient ring ofR. It is shown that ifAis a finite normalizing quasi-Frobenius extension ofB, thenQr(A) =Ql(A) if and only ifQr(B) =Ql(B).

ISSN:0092-7872    

DOI:10.1080/00927879808826269

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1998

数据来源: Taylor

摘要:

In this paper we obtain characterizations of classes of semirings byP-injective and projective rightR-semimodules. We prove that a semiringRis von Neumann regular if and only if each cyclic rightR-semimodule isP-injective. Moreover, a commutative semiring R whose principal ideals arek-closed is von Neumann regular if and only if every simpleR-semimodule is PP-injective. We also examine some properties of rightPP-semirings, that is, semirings all of whose principal right ideals are projective. It is shown thatRis a rightPP-semiring if and only if the endomorphism semiring of every cyclic projective rightR-semimodule is rightPP.

ISSN:0092-7872    

DOI:10.1080/00927879808826270

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1998

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879808826271

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1998

数据来源: Taylor

摘要:

We examine the Weyl invariant subringH*(BT)Wof the integral singular cohomology ringH*(BT) of the classifying spaceBTof the maximal torusTin a connected compact Lie groupK. We show thatH*(BT)Wis not a polynomial algebra forK= Spin(n) whenn≥10. We describe the connection of this result with the Borel homomorphismH*{BT) →H*{K/T).

ISSN:0092-7872    

DOI:10.1080/00927879808826272

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1998

数据来源: Taylor

摘要:

In this paper we define a concept of equisingularity for families of plane curves in any characteristic. For this, we give a natural generalization of Zariski's equisingularity in the case of plane curves over non algebraically closed fields. This new concept avoids the pathologies in positive characteristic of Zariski's theory. We prove that Zariski's concept is a particular case of ours and we also see that the new one is an open condition.

ISSN:0092-7872    

DOI:10.1080/00927879808826273

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1998

数据来源: Taylor

摘要:

We prove a number of results concerning Armendariz rings and Gaussian rings. Recall that a (commutative) ringRis (Gaussian) Armendariz if for two polynomialsf,g∈R[X] (the ideal ofRgenerated by the coefficients off gis the product of the ideals generated by the coefficients offandg)fg= 0 impliesaibj=0 for each coefficientaioffandbjofg. A number of examples of Armendariz rings are given. We show thatRArmendariz implies thatR[X] is Armendariz and that forRvon Neumann regularRis Armendariz if and only ifRis reduced. We show thatRis Gaussian if and only if each homomorphic image ofRis Armendariz. Characterizations of whenR[X] andR[X] are Gaussian are given.

ISSN:0092-7872    

DOI:10.1080/00927879808826274

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1998

数据来源: Taylor

摘要:

Let δ be a derivation in a fieldKof characteristic 0, with fixed fieldk. We show that, ifK/kis finitely generated, then the codimension, ask-vector space, ofKδ +kinKis infinite, while in the infinitely generated case, the said codimension can be any finite non-negative integer.

ISSN:0092-7872    

DOI:10.1080/00927879808826275

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1998

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879808826276

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1998

数据来源: Taylor

摘要:

We generalize Lie bialgebras and Lie bialgebioids to new objects which we call generalized Lie bialgebras. Similar to Lie bialgebras and Lie bial-gebroids, generalized Lie bialgebras are self-dual and generate canonically Hamiltonian structures on their representative spaces. We show that for a generalized Lie bialgebra (E, Ē), a pair (L1,L2) ofE+Ē is again a generalized Lie bialgebra iff (L1,L2) is a Dirac structure pair . Construction of generalized Lie bialgebras by using Poisson tensors and Hamiltonian operators are also discussed in detail and an example relating to an infinite-dimensional integrable system is given.

ISSN:0092-7872    

DOI:10.1080/00927879808826277

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1998

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879808826278

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1998

数据来源: Taylor