Local Jordan Derivations and Local Jordan Automorphisms of Upper Triangular Matrix Algebras
Received:March 12, 2008  Revised:January 05, 2009
Key Words: local Jordan derivations   local Jordan automorphisms   local derivations   local automorphisms   upper triangular matrix algebras.  
Fund Project:Supported by the Doctor Foundation of Henan Polytechnic University (Grant No.B2010-93).
Author NameAffiliation
Yan Xia ZHAO School of Mathematics and Information Science, Henan Polytechnic University, Henan 454000, P. R. China 
Rui Ping YAO Department of Mathematics, China University of Mining and Technology, Jiangsu 221008, P. R. China 
Deng Yin WANG Department of Mathematics, China University of Mining and Technology, Jiangsu 221008, P. R. China 
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Abstract:
      Let $R$ be a commutative ring with identity, $T_{n}(R)$ the $R$-algebra of all upper triangular $n$ by $n$ matrices over $R$. In this paper, it is proved that every local Jordan derivation of $T_{n}(R)$ is an inner derivation and that every local Jordan automorphism of $T_{n}(R)$ is a Jordan automorphism. As applications, we show that local derivations and local automorphisms of $T_{n}(R)$ are inner.
Citation:
DOI:10.3770/j.issn:1000-341X.2010.03.011
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