ISSN:0092-7872    

DOI:10.1080/00927870008827150

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

In this paper,we investigate power-substitution over exchange rings.We show that an exchange ringRsatisfies power-substitution if and only if for any regularx ∈ R, there exists a positive integernsuch thatxInis unit πregular inMn(R).

ISSN:0092-7872    

DOI:10.1080/00927870008827151

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

This paper gives decidable conditions for when a finitely generated subgroup of a free group is the fundamental group of a Schützenberger automaton corresponding to a monoid presentation of an inverse monoid. Also, generalizations are given to specific types of inverse monoids as well as to monoids which are "nearly inverse." This result has applications to computing membership for inverse monoids in a Mal'cev product of the pseudovariety of semilattices with a pseudovariety of groups.

ISSN:0092-7872    

DOI:10.1080/00927870008827152

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927870008827153

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927870008827154

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

In this article we consider several aspects of algebraic combinatorics and combinatorial algebra over fields of prime characteristics.P-super-Radford theorem gives the structure of the free associative algebra over a field of prime characteristic with the new multiplication given by the super shuffle product, we show that this algebra is isomorphic to the reduced free super commutative algebra ons-regular words. We prove the elimination theorem for free partially commutative color Liep-superalgebras and obtain a Schreier type formula for free Liep-superalgebras using formal power series techniques.

ISSN:0092-7872    

DOI:10.1080/00927870008827155

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

We find the full normalizer of γ1(N) in psl2(R).

ISSN:0092-7872    

DOI:10.1080/00927870008827156

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

A result of Ginn and Moss asserts that a left and right noetherian ring with essential right socle is left and right artinian. There are examples of right finitely embedded rings with ACC on left and right annihilators which are not artinian. Motivated by this, it was shown by Faith that a commutative, finitely embedded ring with ACC on annihilators (and square-free socle) is artinian (quasi-Frobenius).AringRis called right minsymmetric if, wheneverkRis a simple right ideal ofR, thenRkis also simple. In this paper we show that a right noetherian right minsymmetric ring with essential right socle is right artinian. As a consequence we show that a ring is quasi-Frobenius if and only if it is a right and left mininjective, right finitely embedded ring with ACC on right annihilators. This extends the known work in the artinian case, and also extends Faith's result to the non-commutative case.

ISSN:0092-7872    

DOI:10.1080/00927870008827157

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

Given an element γ in a group γ, the stable exponent p+(γ) of γ is defined as p+(γ) =lim supn→∞P(γn) denotes the exponent of P(γn) = sup{k/ ∀γo∈ γ such that γn= γkoWe prove that if γ acts properly discontinuously by isometrics on a proper geodesic Gromov-hyperbolic metric space and γ ∈ γ is of hyperbolic type, then P+(γ) is an integer. This implies that the stable exponent of every element of infinite order in a word hyperbolic group is an integer. We also show that, in a translation discrete group, the stable exponent of every element of infinite order is finite.

ISSN:0092-7872    

DOI:10.1080/00927870008827158

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

LetKbe a fieldandsets of indetorminates, andf∈k[[x]]g∈k[[Y]] two non-zero formal power series withf∈ (x)g∈ (Y). Setand suppose that δgis a (y)-primary ideal (e.g., if charK= 0 and g is an isolated singularity). WriteR=K[[X,Y]]/(f+g)R1=k[[X]]/(f) and [Rtilde]:=R/δgR. The main aim of this paper is to relate an arbitrary maximal Cohen-Macaulay (MCM for short)R-moduleNto the higher order syzygy, and in this way relate indecomposable MCMR-modules to higher order syzygies of certain indecomposable[Rtilde]-modules. The[Rtilde]-modules in question are deformations of MCMR-modules and are weakly liftablc. We find resolutions of the higher order syzygy modules in question which are shown to be minimal in certain situations, and express these in terms of matrix factorizations. The theory is shown to be applicable with almost complete success to singularities of KnOrrer-type and, in any case, to give detailed information about MCMR-modules.

ISSN:0092-7872    

DOI:10.1080/00927870008827159

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor