摘要:

The following paper shows the algebraic structure of Archimedean lattice-ordered rings in which a product of anynelements is comparable with zero (or n-orderpotent rings). It is shown that such rings are necessarily subdirect products of nilpotent e-rings and totally-ordered ones. If a given ring is also anf-ring, then it is a direct cardinal product of an Archimedean zero-ring and a subring of the reals.

ISSN:0092-7872    

DOI:10.1080/00927879308824779

出版商:Marcel Dekker, Inc.    

年代:1993

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879308824780

出版商:Marcel Dekker, Inc.    

年代:1993

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879308824781

出版商:Marcel Dekker, Inc.    

年代:1993

数据来源: Taylor

摘要:

The object of our investigation is the canonical operation of the automorphism group of a formally real fieldFonXF, the space of orderings ofF. For a naturally distinguished class of formally real fields, the so-called real-local fields, the Baer-Krull-bijection induces onXFthe structure of a module over the endomorphism ring of the group of archimedean classes ofF. We show that AutFacts onXFby affinities with respect to that module structure. Subsequently, this “arithmetization” of the operation is exemplarily applied to the question of transitivity (“When can any two orderings ofFbe transformed into each other by some automorphism ofF?"), and to the investigation of the subgroup of AutFgenerated by all order automorphism groups ofF.

ISSN:0092-7872    

DOI:10.1080/00927879308824782

出版商:Marcel Dekker, Inc.    

年代:1993

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879308824783

出版商:Marcel Dekker, Inc.    

年代:1993

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879308824784

出版商:Marcel Dekker, Inc.    

年代:1993

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879308824785

出版商:Marcel Dekker, Inc.    

年代:1993

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879308824786

出版商:Marcel Dekker, Inc.    

年代:1993

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879308824787

出版商:Marcel Dekker, Inc.    

年代:1993

数据来源: Taylor

摘要:

Hajós proved that if a finite abelian group is a direct product of cyclic subsets, then at least one of the factors is a subgroup of the group. A cyclic subset consists of the “first some consecutive elements” of a cyclic subgroup. We give a generalization for Hajós' theorem. The proof of this generalization is simpler and the steps are better motivated than the proof of the original result.

ISSN:0092-7872    

DOI:10.1080/00927879308824788

出版商:Marcel Dekker, Inc.    

年代:1993

数据来源: Taylor