On prime and semiprime rings with permuting 3-derivations

被引：22

作者：

Jung, Yong-Soo ^{[1
]}

Park, Kyoo-Honc ^{[2
]}

机构：

[1] Sun Moon Univ, Dept Math, Chungnam 336708, South Korea

[2] Seowon Univ, Dept Math Educ, Chungbuk 361742, South Korea

来源：

BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY | 2007年 / 44卷 / 04期

关键词：

prime ring; semiprime ring; commuting map; centralizing map; derivation; bi-derivation; 3-derivation;

D O I：

10.4134/BKMS.2007.44.4.789

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let R be a 3-torsion free semiprime ring and let I be a nonzero two-sided ideal of R. Suppose that there exists a permuting 3-derivation Delta : R x R x R -> R such that the trace is centralizing on I. Then the trace of Delta is commuting on I. In particular, if R is a 3!-torsion free prime ring and Delta is nonzero under the same condition, then R is commutative.

引用

页码：789 / 794

页数：6

共 5 条

[1] Commuting maps: A survey
Bresar, M
[J]. TAIWANESE JOURNAL OF MATHEMATICS, 2004, 8 (03): : 361 - 397
[2] Joso V., 1989, Aequationes Math., V38, P245, DOI 10.1007/BF01840009
[3] Joso V., 1990, Aequationes Math., V40, P181, DOI [10.1007/BF02112294, DOI 10.1007/BF02112294]
[4] CENTRALIZING MAPPINGS OF PRIME-RINGS
MAYNE, JH
[J]. CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 1984, 27 (01): : 122 - 126
[5] Posner E. C., 1957, P AM MATH SOC, V8, P1093, DOI [DOI 10.1090/S0002-9939-1957-0095863-0, 10.1090/S0002-9939-1957-0095863-0]

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