PRESERVING ZEROS OF A POLYNOMIAL

被引：8

作者：

Guterman, A. E. ^{[1
]}

Kuzma, B. ^{[2
,3
]}

机构：

[1] Moscow MV Lomonosov State Univ, Fac Algebra, Dept Math & Mech, Moscow 119991, Russia

[2] Univ Primorska, FAMNIT, Koper, Slovenia

[3] Inst Math Phys & Mech, Ljubljana, Slovenia

来源：

COMMUNICATIONS IN ALGEBRA | 2009年 / 37卷 / 11期

关键词：

Matrix algebra; Multilinear polynomials; Preservers; LINEAR-MAPS; OPERATOR-ALGEBRAS; ADDITIVE MAPS; MATRICES; MAPPINGS; COMMUTATIVITY; PRODUCTS; TRANSFORMATIONS; DERIVATIONS;

D O I：

10.1080/00927870802545687

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study nonlinear surjective mappings on M(n)(IF) and its subsets, which preserve the zeros of some fixed polynomials in noncommuting variables.

引用

页码：4038 / 4064

页数：27

共 38 条

[1] Rank-permutable additive mappings [J].

Alieva, AA ;

Guterman, AE ;

Kuzma, B .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2006, 414 (2-3) :607-616

[2]

AMITSUR SA, 1950, P AM MATH SOC, V1, P449

[3] Linear preservers of zeros of matrix polynomials [J].

Beasley, LB ;

Guterman, AE ;

Lee, SG ;

Song, SZ .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2005, 401 :325-340

[4] LINEAR-OPERATORS PRESERVING IDEMPOTENT MATRICES OVER FIELDS [J].

BEASLEY, LB ;

PULLMAN, NJ .

LINEAR ALGEBRA AND ITS APPLICATIONS, 1991, 146 :7-20

[5] On surjective linear maps preserving commutativity [J].

Beidar, KI ;

Lin, YF .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2004, 134 :1023-1040

[6] On additive isomorphisms of prime rings preserving polynomials [J].

Beidar, KI ;

Fong, Y .

JOURNAL OF ALGEBRA, 1999, 217 (02) :650-667

[7]

Bhatia R, 1997, B LOND MATH SOC, V29, P1

[8] LINEAR TRANSFORMATIONS THAT PRESERVE THE NILPOTENT MATRICES [J].

BOTTA, P ;

PIERCE, S ;

WATKINS, W .

PACIFIC JOURNAL OF MATHEMATICS, 1983, 104 (01) :39-46

[9] LINEAR TRANSFORMATIONS PRESERVING POTENT MATRICES [J].

BRESAR, M ;

SEMRL, P .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1993, 119 (01) :81-86

[10] MAPPINGS WHICH PRESERVE IDEMPOTENTS, LOCAL AUTOMORPHISMS, AND LOCAL DERIVATIONS [J].

BRESAR, M ;

SEMRL, P .

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 1993, 45 (03) :483-496

← 1 2 3 4 →