1. |
Properness, strictness, and nilness in jordan systems |
|
Communications in Algebra,
Volume 27,
Issue 7,
1999,
Page 3041-3066
Kevin McCrimmon,
Preview
|
PDF (1045KB)
|
|
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
|
2. |
Strict proper nilness modulo an absorber |
|
Communications in Algebra,
Volume 27,
Issue 7,
1999,
Page 3067-3091
Kevin McCrimmon,
Preview
|
PDF (839KB)
|
|
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
|
3. |
Henselian valued quasi-local fields with totally indivisible value groups |
|
Communications in Algebra,
Volume 27,
Issue 7,
1999,
Page 3093-3108
I.D. Chipchakov,
Preview
|
PDF (705KB)
|
|
ISSN:0092-7872
DOI:10.1080/00927879908826612
出版商:Gordon and Breach Science Publishers Ltd.
年代:1999
数据来源: Taylor
|
4. |
Automorphism and similarity groups of forms determined by the characteristic polynomial |
|
Communications in Algebra,
Volume 27,
Issue 7,
1999,
Page 3109-3116
Adam Wesolowski,
Preview
|
PDF (243KB)
|
|
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
|
5. |
Kawamata-viehweg vanishing and quint-canonical map of a complex threefold |
|
Communications in Algebra,
Volume 27,
Issue 7,
1999,
Page 3117-3128
Meng Chen,
Preview
|
PDF (413KB)
|
|
ISSN:0092-7872
DOI:10.1080/00927879908826614
出版商:Gordon and Breach Science Publishers Ltd.
年代:1999
数据来源: Taylor
|
6. |
On derivations of prime rings* |
|
Communications in Algebra,
Volume 27,
Issue 7,
1999,
Page 3129-3135
Matej Brešar,
M. A. Chebotar,
Peter Šemrl,
Preview
|
PDF (242KB)
|
|
ISSN:0092-7872
DOI:10.1080/00927879908826615
出版商:Gordon and Breach Science Publishers Ltd.
年代:1999
数据来源: Taylor
|
7. |
Star operations and primitive polynomials |
|
Communications in Algebra,
Volume 27,
Issue 7,
1999,
Page 3137-3142
D.D. Anderson,
Muhammad Zafrullah,
Preview
|
PDF (243KB)
|
|
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
|
8. |
On finite groups with few non-normal subgroups |
|
Communications in Algebra,
Volume 27,
Issue 7,
1999,
Page 3143-3151
H. Mousavi,
Preview
|
PDF (225KB)
|
|
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
|
9. |
The half-factorial property in integral extensions |
|
Communications in Algebra,
Volume 27,
Issue 7,
1999,
Page 3153-3159
Jim Coykendall,
Preview
|
PDF (203KB)
|
|
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
|
10. |
On radicals of a left-symmetric algebra |
|
Communications in Algebra,
Volume 27,
Issue 7,
1999,
Page 3161-3175
Kyeong Soo Cheng,
Hyuk Kim,
Hyo Chul Myung,
Preview
|
PDF (541KB)
|
|
ISSN:0092-7872
DOI:10.1080/00927879908826619
出版商:Gordon and Breach Science Publishers Ltd.
年代:1999
数据来源: Taylor
|