摘要:

Forka field.Hak-bialgebra andCa rightH-modulek-coalgebra, we define a new comultiplication on theH-moduleCto obtain a “twisted coalgebra”.. If τ is invertible. the categories of relative right Hopf modules over C andare isomorphie. We show that crossed coproducts are invertible twistings of the tensor coalgebras. These results arc dual to [1. Theroem 1.1] and [l. Theorem3.4].

ISSN:0092-7872    

DOI:10.1080/00927870008841074

出版商:Marcel Dekker, Inc.    

年代:2000

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927870008841075

出版商:Marcel Dekker, Inc.    

年代:2000

数据来源: Taylor

摘要:

In this paper we study the question of when anH-comodule algebra is a faithfully flat Galois extension of its sub algebra of coinvariants for certain Hopf algebrasH. We note that ifHis connected, a faithfully flat Galois extension must actually be cleft and hence a crossed product, and we show that with a different hypothesis, a faithfully flat Galois extension must be a smash product. We also describe faithfully flat Galois extensions whenHis pointed cocommutative. We give an explicit description ofH-comodule algebras whenHis a polynomial algebra, a divided power Hopf algebra, a free algebra, or a shuffle algebra. We give necessary and sufficient conditions for anH-extension to be faithfully flat Galois in these cases and in the case whereHis the enveloping algebra of a Lie algebra; a key ingredient in our analysis is the existence and description of a total integral. In the case where, we give a simple example of a flat Galois extension that is not faithfully flat.

ISSN:0092-7872    

DOI:10.1080/00927870008841076

出版商:Marcel Dekker, Inc.    

年代:2000

数据来源: Taylor

摘要:

We know that, in general, an algebra satisfying an Engel's condition is a nilalgebra. But an Engel's condition don't implies necessarily the nilpotency of the algebra. In this paper we show that every Bernstein algebra satisfying the second or the third Engel's condition is genetic, that is, the kernel of his weight fonction is nilpotent. This is also the case for a Bernstein algebra satisfying the second weak Engel's condition.

ISSN:0092-7872    

DOI:10.1080/00927870008841077

出版商:Marcel Dekker, Inc.    

年代:2000

数据来源: Taylor

摘要:

LetGbe a finite group andMa maximal subgroup ofG. A θ-completion ofMinGis any subgroupCsuch thatCis not contained inMwhileMG, the core ofMinG, is contained inCandhas no proper normal subgroup of. The concept of θ -completion offers a convenience for us to study the Deskins completions. By using this concept and in a quite different way from what was used, we obtain some new results about the maximal completions and θ-completions which implyGto be solvable and supersolvable.

ISSN:0092-7872    

DOI:10.1080/00927870008841078

出版商:Marcel Dekker, Inc.    

年代:2000

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927870008841079

出版商:Marcel Dekker, Inc.    

年代:2000

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927870008841080

出版商:Marcel Dekker, Inc.    

年代:2000

数据来源: Taylor

摘要:

In the first part of this paper, we give necessary and sufficient conditions for a quasi-projective module whose endomorphism ring has the powersubstitution property, by way of completion of diagrams. In the second part, we study exchange rings with the right power-substitution property. We prove that for any moduleMwith the finite exchange property, the ringEndRR(M) has the right power-substitution property if (and only if)Mhas the power cancellation property, if and only if for any regular element, there exists an integersuch thataInis unit-regular in

ISSN:0092-7872    

DOI:10.1080/00927870008841081

出版商:Marcel Dekker, Inc.    

年代:2000

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927870008841082

出版商:Marcel Dekker, Inc.    

年代:2000

数据来源: Taylor

摘要:

Margolis and Meakin use the Cayley graph of a group presentation to constructE-unitary inverse monoids [11]. This is the technique we refer to asgraph expansion. In this paper we consider graph expansions ofunipotentmonoids, where a monoid is unipotent if it contains a unique idempotent. The monoids arising in this way areE-unitary and belong to the quasivariety ofweakly left amplemonoids. We give a number of examples of such monoids. We show that the least unipotent congruence on a weakly left ample monoid is given by the same formula as that for the least group congruence on an inverse monoid and we investigate the notion ofproperfor weakly left ample monoids.

ISSN:0092-7872    

DOI:10.1080/00927870008841083

出版商:Marcel Dekker, Inc.    

年代:2000

数据来源: Taylor