摘要:

It is well known that the semigroup of all transformations on a finite setXof ordernis generated by its group of units, the symmetric group, and any idempotent of rankn− 1. Similarly, the symmetric inverse semigroup onXis generated by its group of units and any idempotent of rankn− 1 while the analogous result is true for the semigroup of all n × n matrices over a field.

ISSN:0092-7872    

DOI:10.1080/00927879808826145

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1998

数据来源: Taylor

摘要:

Anodality (also termed u-closedness) is a notion coming from K-theory and is usefull when studying Pic A[X, X-1]. An injective ring morphismA→Bis called anodal if an elementxinBbelongs toAwheneverThen a ringAwith total quotient ringKis said to be anodal ifA→Kis anodal. We show that a weak Baer ringAis anodal if and only if for each pair (a, b) ∈ A2such thatthere is some z ∈Asuch that. Anodality of weak Baer rings is descended by faithfully flat or anodal morphisms. We defineu-integral morphisms similar toR. Swan's subintegral morphisms and show that for any injective morphismA→Bthere is a u-closuresuch thatis u-integral. A u-integral morphism is locally an epimorphism and is a direct limit of unramified morphisms. This result has many consequences. An injective integral morphism which is injective on the spectrum is locally anodal whence anodal. If A is a weak Baer ring, then A is locally anodal if A is locally unibranched; the converse is true if, in addition, A is one-dimensional and Noetherian. We introduce new closures for injective ring morphismsA→Bin order to evaluate. In some measure, seminormality and anodality are dual notions : among other results, we get that Picfis injective for a u-integral ring morphismf, while Picfis surjective iffis subintegral.

ISSN:0092-7872    

DOI:10.1080/00927879808826134

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1998

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879808826135

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1998

数据来源: Taylor

摘要:

We define a notion of polynomial identity for Poisson algebras. A multilinearization process is described and symplectic algebras are characterized by their identities.

ISSN:0092-7872    

DOI:10.1080/00927879808826136

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1998

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879808826137

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1998

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879808826138

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1998

数据来源: Taylor

摘要:

Leibniz algebras are in some sense non-(anti)commutative analogs of Lie algebras. The variety of all Lie algebras has the Schreier property (i.e. any subalgebra of the free algebra is free). This is not the case in the variety of all Leibniz algebras. Nevertheless we prove that:

ISSN:0092-7872    

DOI:10.1080/00927879808826139

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1998

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879808826140

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1998

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879808826141

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1998

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879808826142

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1998

数据来源: Taylor