摘要:

In this paper we are dealing with associative triple systems of second kind in Loos' notation. We develop a general theory of the sacle paralleling that for associative and Jordan algebras and give a structure theorem for semiprime associative triple systems whose socle is an essential ideal. In particular we prove that every prime associative triple system A containing minimal inner ideals is isomorphic to a triple of continuous linear operators containing all finite rank operators L(x,y) ⊃A⊃ F(x,y) where X,Y are nomlegenerate inner product spaces overa unital associative algebra with involution (δT), where x,y are hermitian and either (1)δ=δ1is a division algebra or (2) δ=δ1⨁δ1opwith the exchange involution,or(3) X,Y are alternate δ = K isafield with the identity as involution. Finally we classify semi prime associative triple systems with descending chain condition on left (right) ideals. In particular, the structure theorem of Lms for semiprime associative triple systems with descendingchain condition on all inner ideels a n be derived from our results.

ISSN:0092-7872    

DOI:10.1080/00927879008823901

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879008823902

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

摘要:

Let V=V0: be a vector space over a field F wit11 associated spaces of linear functionals V1, V2, V3, V4, Vjbelonging to Hom (Vj-1,F).In this paper we generalize the procedure used to extend a binary product on V to one on V2,focusing here on the case where V is a triple system. As in the case of binary algebras we have a space [Vbreve] (called the closure of V), a subtriple system of V2whlich satisfies the same multilinear identies as V. 1n paritcular, if V is a Jordan triple system and the characteristic of F is not two or three, then ˘ isalso a Jordan triple system; if V is a Lie triple system, then [Vbreve] is also a Lie triple system.

ISSN:0092-7872    

DOI:10.1080/00927879008823903

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879008823904

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879008823905

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879008823906

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879008823907

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879008823908

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

摘要:

LetRbe a commutative ring and letFbe a filter of ideals ofR. We give three characterizations of the rings with the property that all finitely generated F pretorsionRmodules decompose into a direct sum of cyclicRsubmodules. One of these characterizations involves decomposing the filterFinto a product of subfilters. This filter decomposition is shown to be unique, and is used to characterize several other ring properties relative to the filter of ideals.

ISSN:0092-7872    

DOI:10.1080/00927879008823909

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879008823910

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor