摘要:

The basic theme of this paper, suggested by Ottmar Loos, is to show that certain setsSofelements in a Jordan systemJform an ideal by showing thatS=J∩R([Jtilde]) is the Amitsur shrinkage of some well-knownl radicalRon some extension[Jtilde]ofJ. The Jacobson radical Rad(J) and the degenerate radical Deg(J) have elemental characterizations as (respectively) the properly quasi-invertible elements and the m-finite elements. Frojn these two characterizations we show that: (1) the strictly properly nilpotent elements coincide with the strictly properly quasi-invertible elements and form the idealJ∩Rad(J[T]) (2) the strictly m-finite elements coincide with the m-finite elements and form the idealDeg:(J) (3) the m-bounded elements form an idealJ∩Deg(Seq(J)) (Seq the algebra of sequences); and (4) the strictly m-bounded elements coincide with the strictly properly nilpotence-bounded elements and form the idealJ∩Deg(Seq(J[t])). We show that all these constructions are stable under structural pairs, a useful generalization of the concept of structural transformation. The question of whether the properly nilpotent elements form an ideal, and if so whether this is the nil radical, is an open question intimately related to the Kothe Conjecture for associative algebras.

ISSN:0092-7872    

DOI:10.1080/00927879908826610

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

摘要:

An elementzof a Jordan systemJis strictly properly nilpotent if it is nilpotent in all homotopes of all extensions ofJ; it is strictly properly nilpotent of bounded index if there is a bound on its indices of nilpotence in all these extensions. We showed in a previous paper that the strictly properly nilpotent elements (resp. those of bounded index) form an ideal, by exhibiting that ideal as an Amitsur shrinkage. In this paper we prove by combinatorial methods (the exponential law for power series and Jordan Binomial Theorems) a modular generalization of this: the elements strictly properly nilpotent (resp. boundedly so) modulo the absorberQof an inner idealKform an ideal. As a corollary we obtain Zelmanov’s Nilness-mod-the-Absorber-Theorem that the ideal generated byQis nil modK. From this we re-derive his Primitive Absorber and Exceptional Heart Theorems (improved to show the heart isS(J), not justS( (J)3), two results crucial to the structure of primitive Jordan systems, using a triple-system version of Zelmanov's KKT-specialization for inner ideals in a Jordan pair.

ISSN:0092-7872    

DOI:10.1080/00927879908826611

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879908826612

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

摘要:

The paper is concerned with forms of degree higher than two. M.Oryan and D.B.Shapiro [OS] proved that ifAis a central simple algebra over a fieldK, ’tr‘ denotes its reduced trace andd≥ 3, then every similarity of the trace formtr(Xd) of degreedonAis standard.

ISSN:0092-7872    

DOI:10.1080/00927879908826613

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879908826614

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879908826615

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

摘要:

LetDbe an integral domain with quotient fieldK. We investigate conditions under which certain primitive polynomials are products of principal primes. Let * be a finite character star operation onD[X] (e.g., * =dort) and let * also denote the star operation induced onDbyI*= (I[X])*∩KwhereIdenotes a nonzero fractional ideal ofD. Then the following conditions are equivalent: (1)Dis integrally closed and each *-invertible *-ideal is principal, (2) IfPis a prime upper to 0 containing anf∈D[X] with, thenPis principal, and (3) Forf∈D[X] withfis a product of principal primes.

ISSN:0092-7872    

DOI:10.1080/00927879908826616

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

摘要:

In this paper we characterize the finite groups having exactly two conjugacy classes of non-normal subgroups.

ISSN:0092-7872    

DOI:10.1080/00927879908826617

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

摘要:

In this paper, the integral closure of a half-factorial subring of a ring of algebraic integers is studied. Theboundary map, a natural generalization of the length function of Zaks, is used to show that the integral closure of such an order is again an HFD.

ISSN:0092-7872    

DOI:10.1080/00927879908826618

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879908826619

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor