摘要:

By a well-known result of Osofsky [6, Theorem] a ring R is semisimple (i.e. R is right artinian and the Jacobson radical of R is zero) if and only if every cyclic right R-module is injective. Starting from this, a larger class of rings has been introduced and investigated, namely the class of right PCI rings. A ring R is called right PCI if every proper cyclic right R- module is injective (proper here means not being isomorphic to RR). By [l] and [Z], a right PCI ring is either semisimple or it is a right noetherian, right hereditary simple ring. The latter ring is usually called a right PCI domain. In this paper we consider the similar question in studying rings whose cyclic right modules satisfy some decomposition property. The starting point is a theorem recently proved in 13, Theorem 1.1): A ring R is right artinian if and only if every cyclic right R- module is a direct sum of an injective module and a finitely cogenerated module.

ISSN:0092-7872    

DOI:10.1080/00927879008823935

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879008823936

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879008823937

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

摘要:

In this paper, the authors continue their investigation of loops which give rise to alternative loop rings. If the coefficient ring has characteristic 2, these loops turn out to form a surprisingly wide class, in contrast to the situation of characteristic ≠ 2. This paper describes many properties of this class, includes diverse examples of Moufang loops which are united by the fact that they have loop rings which are alternative, and discusses analogues in loop theory of a number of important group theoretic constructions.

ISSN:0092-7872    

DOI:10.1080/00927879008823938

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879008823939

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

摘要:

In this paper we show that strong noncommutative Jordan algebras R over an arbitrary ring of scalars having the alternator mappings y,y,-1 as Jordon derivations are U-algebras, algebras such that Uablpar;crpar; lies in the Jordan ideal generated by a. For any U-algebra R we relate the radical theories of R and R+. Our main result is that any radical property p′ of U-algebras such that P′-radR⊂ p-radR+. If p is nondegenerate the P′ is nondegenerate and P′-radR=p-radR+. This applies in particular to the McCrimmon, locally nilpotent, nil, Jacobson and Brown-McCoy radicals of Jordan algebras

ISSN:0092-7872    

DOI:10.1080/00927879008823940

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

摘要:

A quadratic formholds for all x represented by φ. This notion was introduced by Witt, and round forms have been an object of research ever since cf.3,6,7,and 10. It turns out that they are also important in the geometric theory of quadratic forms: The group of similarities of a metric vector space (V,K,q) (char K≠2) operates transitively on the set non-singular vectors iff the form q is round up to a nonzero factor. Using this we get a similar description of the transitivity behaviour of several other metric collineation groups (cf.[2]). Semisimilarities of (V.K.q) are exactly those semilinear bijections which preserve the orthogonality relation provided byq. To study the transitivity properites of the group of semisimilarities the notion of a semiround form was introduced in [2]: A form φ is called semiround if for all x represented by φ there is a field automorphism σ of the underlying fieldKsuch that. In [2] we have shown that the group of semisimilarities of (V,K,q) (char K≠2) operates transitively on the set of non-singular vectors iff q is semiround up to a nonzero factor. Hence, these forms are also worth further investigation.

ISSN:0092-7872    

DOI:10.1080/00927879008823941

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879008823942

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879008823943

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879008823944

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor