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Czechoslovak Mathematical Journal

, Volume 64, Issue 2, pp 335–350 | Cite as

The group of commutativity preserving maps on strictly upper triangular matrices

  • Dengyin Wang
  • Min Zhu
  • Jianling Rou
Article

Abstract

Let N = N n (R) be the algebra of all n × n strictly upper triangular matrices over a unital commutative ring R. A map φ on N is called preserving commutativity in both directions if xy = yxφ(x)φ(y) = φ(y)φ(x). In this paper, we prove that each invertible linear map on N preserving commutativity in both directions is exactly a quasi-automorphism of N, and a quasi-automorphism of N can be decomposed into the product of several standard maps, which extains the main result of Y. Cao, Z. Chen and C. Huang (2002) from fields to rings.

Keywords

commutativity preserving map automorphism commutative ring 

MSC 2010

17C30 15A04 15A27 15A99 13C10 

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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2014

Authors and Affiliations

  1. 1.Department of MathematicsChina University of Mining and TechnologyXuzhouP.R. China

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