摘要:

LetLbe a Lie algebra, nilpotent of class 2, over an infinite fieldK, and suppose that the centreCofLis one dimensional; such Lie algebras are called Heisenberg algebras. Let ρ:L→homKVbe a finite dimensional representation of the Heisenberg algebraLsuch that ρ(C) contains non-singular linear transformations ofV, and denotel(ρ) the ideal of identities for the representation ρ. We prove that the ideals of identities of representations containingI(ρ) and generated by multilinear polynomials satisfy the ACC. Letsl2(L) be the Lie algebra of the traceless 2×2 matrices overK, and suppose the characteristic ofKequals 2. As a corollary we obtain that the ideals of identities of representations of Lie algebras containing that of the regular representation ofsl2(K) and generated by multilinear polynomials, are finitely based. In addition we show that one cannot simply dispense with the condition of multilinearity. Namely, we show that the ACC is violated for the ideals of representations of Lie algebras (over an infinite field of characteristic 2) that contain the identities of the regular representation ofsl2(K).

ISSN:0092-7872    

DOI:10.1080/00927870008827012

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

Many concepts of analytic spread for filtrations exist in the current literature. As far as we know, none of them is explicitly of asymptotic nature. Here we give a definition of analytic spread for filtrations which is shown to be of asymptotic nature.

ISSN:0092-7872    

DOI:10.1080/00927870008827013

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

Let [n] = {1,2,…,n} be a finite set, ordered in the usual way. Theorder-preserving transformation semigroup Onis the set of all order-preserving transformations of [n] (excluding the identity mapping) under composition. In this paper we first describe maximal idempotent-generated subsemigroups ofOn, and show thatOnhas 2n- 2 such subsemi-groups. Secondly, we investigate maximal regular subsemigroups ofOn, and obtain the number of such subsemigroups as 2n- 3. Thirdly, we describe maximal idempotent-generated regular subsemigroups ofOn, and also obtain their classification and number.

ISSN:0092-7872    

DOI:10.1080/00927870008827014

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

LetRk[x1,x2,x3] be a 3-dimensional polynomial ring over a fieldk.We show that no non-trivial relations exist among *-products of complete one-fibered (x1,x2,x3)-primary monomial ideals. This is connected with questions about how Zariski's work on the unique factorization of complete ideals in regular local rings of dimension two might be generalized to higher dimensions.

ISSN:0092-7872    

DOI:10.1080/00927870008827015

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

For a large class of groupsGa precise congruence subgroup of the group generated by the bicyclic units of the integral group ringZGis determined. As an application an upper bound is calculated for the index in the unit group ofZGfor the group generated by the Bass cyclic units and the bicyclic units.

ISSN:0092-7872    

DOI:10.1080/00927870008827016

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

LetAbe a prime ring with involution *Kbe its set of skew element, andRbe a noncentral Lie ideal ofK. Further, letQbe the maximal right ring of quotients ofAandbe maps. We study functional identities of the formfor all(wheremeansetc). In caseAdoes not satisfy the standard identity of degree ≤ 4(m+ 1), definitive results are obtained.

ISSN:0092-7872    

DOI:10.1080/00927870008827017

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

Majid in [14] and Bespalov in [2] obtain a braided interpretation of Radford’s theorem about Hopf algebras with projection ([19]). In this paper we introduce the notion of H-cleft comodule (module) algebras (coalgebras) for a Hopf algebra H in a braided monoidal category, and we characterize it as crossed products (coproducts). This allows us give very short proofs for know results in our context, and to introduce others stated for the category ofR-modules about of Hopf algebra extensions. In particular we give a proof of the result by Bespalov [2] for a braided monoidal category with co(equalizers).

ISSN:0092-7872    

DOI:10.1080/00927870008827018

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

Graded isolated singularities appear very naturally in algebraic pro-jcctive geometry (cf. [18]) or invariant theory of the binary polyhedral groups (cf. [15], [17]). We define mock finitely generated modules in the category of graded modules and we use such graded modules which are also Gorenstein injective (cf. [1], [2]) in this category to characterize graded isolated Gorenstein singularities.

ISSN:0092-7872    

DOI:10.1080/00927870008827019

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

We obtain efficient programs for obtaining representatives of all the conjugacy classes of all the sporadic simple groups except the Monster and the Baby Monster.

ISSN:0092-7872    

DOI:10.1080/00927870008827020

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

We study various types of noncommutative Galois extensions and present some examples. We state a criterion which decides whether a given automorphism of a Galois extension belongs to the corresponding Galois group or not. We then compute Borovoi’s nonabelian cohomology sets (in degree 0, 1, 2) of the Galois group with coefficients in a crossed module associated to the Galois extension.

ISSN:0092-7872    

DOI:10.1080/00927870008827021

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor