摘要:

LetVbe a module over a ringR. We defineVto be a unique addition module (UAM) if it is not possible to change the addition ofVwithout changing the action ofRonV. IfRis a domain such that 1 is not the only unit inRandVis a torsion-free i2-module, then we show thatVis a UAM if and only ifVhas rank 1 (or ifV={0}). We also classify finitely generated unique addition modules over commutative Artinian rings.

ISSN:0092-7872    

DOI:10.1080/00927879908826687

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

摘要:

For an action a of a groupGon an algebraR(over C), the crossed productRxαGis the vector space ofR-valued functions with finite support inG, together with the twisted convolution product given bywherep∈G. This construction has been extended to the theory of Hopf algebras. Given an action of a Hopf algebraAon an algebraR, it is possible to make the tensor productR⊗Ainto an algebra by using a twisted product, involving the action. In this case, the algebra is called the smash product and denoted by R#A. In the group case, the action a ofGonRyields an action of the group algebra CGas a Hopf algebra onRand the crossedRxαGcoincides with the smash productR#CG. In this paper we extend the theory of actions of Hopf algebras to actions of multiplier Hopf algebras. We also construct the smash product and we obtain results very similar as in the original situation for Hopf algebras.

ISSN:0092-7872    

DOI:10.1080/00927879908826688

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879908826689

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

摘要:

In this paper we determine those compatible partial orders on the bicyclic semigroupBwhich turn it into a semilatticed semigroup. We shall see that there are exactly four distinct compatible total orderings onB. These are the only compatible orderings which turnBinto a lattice ordered semigroup.

ISSN:0092-7872    

DOI:10.1080/00927879908826690

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

摘要:

It is shown that every exchange ring satisfying related comparability is separative. This yields that related comparability over exchange rings is Morita invariant. Also we investigate pseudosimilarity over exchange rings satisfying related comparability.

ISSN:0092-7872    

DOI:10.1080/00927879908826691

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

摘要:

LetR(G) denote the intersection of all nonnormal subgroups of a groupG. In this note, we prove that for every finite groupG, ifR(G) is not trivial, then the normalizer property holds forG.

ISSN:0092-7872    

DOI:10.1080/00927879908826692

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

摘要:

Letkbe a field and letAbe an affine, semiprime noetherian λ-algebra of pi degreedand Krull dimension 1. We extend results of [G3] and [GJRW] on the torsion subgroup of Cl(λ), the genus class group of λ. Let Γ be a maximal order containing λ. Then we prove that, if there exists a (λ,Γ) -conductorCwhich is a semiprime ideal of Γ, there is a positive integerm(depending onA) such that Cl(λ)nis finite for all n prime tom, where the subscript denotes thentorsion subgroup. Ifkis a number field or has positive characteristic, then the assumption on the conductor can be dropped. Moreover, we give examples to show that our result is sharp, in the sense that every potential source of infinite torsion identified in the proof actually arises for some λ. Using a change of rings functor of [G2], we can partially extend this result to arbitrary finitely-generated λ-lattices. We prove that, for each positive integerr, there exists an integerm(r)depending onrand λ such thatG(M)nis finite for all n prime tom(r)for any λ-lattice of rankr, whereG(M) is the genus class group of the latticeM. We also prove sharper versions of this result whenkis a number field or has positive characteristic.

ISSN:0092-7872    

DOI:10.1080/00927879908826693

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

摘要:

In this paper, we introduce an important subclass of quasiregular semigroups, namely the class of C*-quasiregular semigroups. This class of semigroups contains the classes of Clifford semigroups, quasi Clifford semigroups, C-quasiregular semigroups and their generalizations as its subclasses. Some characterization theorems for such semigroups are obtained. The structure of this kind of quasiregular semigroups is investigated by using the generalized ▵-product of some semigroups on a semilattice Y. Construction techniques of such classes of semigroups are particularly demonstrated.

ISSN:0092-7872    

DOI:10.1080/00927879908826694

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879908826695

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

摘要:

Letgbe a complex simple Lie algebra with root system ▵. We prove that any classical doubleD (g)is graded by ▵.As a consequence of this fact we obtain thatD (g)≅g⊗A, whereAis a unital com-muative associative algebra of dimension 2. Therefore we have two possibilities forAnilpotent and semisimple. The first case leads to solutions of CYBE and the second case leads to solutions of mCYBE. We obtain an explicit description of Lie bialgebra structures ongin both cases.

ISSN:0092-7872    

DOI:10.1080/00927879908826696

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor