摘要:

In 1963 [Ann. of Math. 78, 267-288], Gerstenhaber invented acomp(osition)calculus in the Hochschild complex of an associative algebra. In this paper, the first steps of the Gerstenhaber theory are exposed in an abstract (comp system) setting. In particular, as in the Hochschild complex, a graded Lie algebra and a pre-coboundary operator can be associated to every comp system. A derivation deviation of the pre-coboundary operator over the total composition is calculated in two ways, (the long) one of which is essentially new and can be seen as an example and elaboration of theauxiliary variables methodproposed by Gerstenhaber in the early days of the comp calculus.

ISSN:0092-7872    

DOI:10.1080/00927870008826902

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

LetGbe an additive group. It is shown that the transformation near-ringdoes not admit nonzero derivations.

ISSN:0092-7872    

DOI:10.1080/00927870008826903

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

For any split exact categoryC, we give an explicit description of the Dennis trace map, from a split model of the algebraicK-theory ofCto the additive cyclic nerve ofC.

ISSN:0092-7872    

DOI:10.1080/00927870008826904

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

We show that a primitive (resp*-primitive) associative algebra having a nonzero PI primitizer (resp. *-primitizer) is necessarily PI Similarly, a primitive Jordan algebra having a PI primitizer with nonzero square is PI.

ISSN:0092-7872    

DOI:10.1080/00927870008826905

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927870008826906

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

LetRbe a commutative ringGa free abelian group of finite ranknandR#Gthe corresponding skew group ring. We fix an integerm; 0 ≤m≤nand a free subgroupGmofGof rankm. We prove that ifRis noetherian, ifspecG(R#Gm) is (R,G)-normally separated and if the Laurent polynomial ringis catenary, then the ringR#GmisG-catenary. In the particular case whereRis an affine algebra over an algebraically closed field, we prove that ifRisG-locally finite, then the skew group ringR#Gmis universally catenary and universallyG-catenary. Furthermore Tauvel's height formula is valid in all prime factors andG-prime factors ofR#Gm.

ISSN:0092-7872    

DOI:10.1080/00927870008826907

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

We study the Hilbert polynomials of finitely generated graded algebrasR, with generators not all of degree one (i.e. non-standard). Given an expressionP(R,t)=a(t)/(1-tl)nfor the Poincare series ofRas a rational function, we study for 0 ≤i≤lthe graded subspaces ⊗kRkl+i(which we denoteR[l;i]) ofR, in particular their Poincaré series and Hilbert functions. We prove, for example, that ifRis Cohen-Macaulay then the Hilbert polynomials of all non-zeroR[l;i] share a common degree. Furthermore, ifRis also a domain then these Hilbert polynomials have the same leading coefficient.

ISSN:0092-7872    

DOI:10.1080/00927870008826908

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

We show that a prime ring satisfies a nontrivial semigroup generalized identity if and only if its central closure is a primitive ring with nonzero socle and the associated skew field is a field.

ISSN:0092-7872    

DOI:10.1080/00927870008826909

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

We describe the maximal subsemigroups of the semigroup of all order-preserving transformations of a finite chain and completely obtain their classification. We also count the number of its maximal subsemigroups.

ISSN:0092-7872    

DOI:10.1080/00927870008826910

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927870008826911

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor