Multiplicative lie isomorphisms between prime rings

被引：32

作者：

Bai, Zhaofang ^{[1
,2
]}

Du, Shuanping ^{[1
,2
]}

Hou, Jinchuan ^{[2
,3
]}

机构：

[1] Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China

[2] Shanxi Normal Univ, Dept Math, Linfen, Peoples R China

[3] Taiyuan Univ Technol, Dept Math, Taiyuan, Peoples R China

来源：

COMMUNICATIONS IN ALGEBRA | 2008年 / 36卷 / 05期

基金：

中国国家自然科学基金;

关键词：

multiplicative Lie isomorphism; prime ring;

D O I：

10.1080/00927870701870475

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let R be a prime ring with 1 containing a nontrivial idempotent E, and let R' be another prime ring. If Phi : R -> R' is a multiplicative Lie isomorphism, then Phi (T + S) = Phi (T) + Phi(S) + Z'(T,S) for all T, S is an element of R, where Z'(T,S) is an element in the center L' of R' depending on T and S.

引用

页码：1626 / 1633

页数：8

共 9 条

[1] LIE ISOMORPHISMS IN PRIME-RINGS WITH INVOLUTION [J].

BEIDAR, KI ;

MARTINDALE, WS ;

MIKHALEV, AV .

JOURNAL OF ALGEBRA, 1994, 169 (01) :304-327

[2] On Herstein's Lie map conjectures, III [J].

Beidar, KI ;

Bresar, M ;

Chebotar, MA ;

Martindale, WS .

JOURNAL OF ALGEBRA, 2002, 249 (01) :59-94

[3] On Herstein's Lie map conjectures, I [J].

Beidar, KI ;

Bresar, M ;

Chebotar, MA ;

Martindale, WS .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2001, 353 (10) :4235-4260

[4] Continuity of Lie isomorpmisms of Banach algebras [J].

Berenguer, MI ;

Villena, AR .

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 1999, 31 :6-10

[5] Lie isomorphisms of non-GPI rings with involution [J].

Blau, PS .

COMMUNICATIONS IN ALGEBRA, 1999, 27 (05) :2345-2373

[6] COMMUTING TRACES OF BIADDITIVE MAPPINGS, COMMUTATIVITY-PRESERVING MAPPINGS AND LIE MAPPINGS [J].

BRESAR, M .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1993, 335 (02) :525-546

[7] On Lie isomorphisms in prime rings with involution [J].

Chebotar, MA .

COMMUNICATIONS IN ALGEBRA, 1999, 27 (06) :2767-2777

[8] LIE ISOMORPHISMS OF PRIME RINGS [J].

MARTINDALE, WS .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1969, 142 (AUG) :437-+

[9] WHEN ARE MULTIPLICATIVE MAPPINGS ADDITIVE [J].

MARTINDALE, WS .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1969, 21 (03) :695-+

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