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DECOMPOSITION OF JORDAN AUTOMORPHISMS OF TRIANGULAR MATRIX ALGEBRA OVER COMMUTATIVE RINGS

Published online by Cambridge University Press:  25 August 2010

XING TAO WANG  and
YUAN MIN LI
XING TAO WANG
Affiliation:
Department of Mathematics, Harbin Institute of Technology, Harbin 150001, P.R. China e-mail: xingtao@hit.edu.cn
YUAN MIN LI
Affiliation:
Department of Mathematics, Harbin Institute of Technology, Harbin 150001, P.R. China e-mail: xingtao@hit.edu.cn
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Abstract

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Let Tn+1(R) be the algebra of all upper triangular n+1 by n+1 matrices over a 2-torsionfree commutative ring R with identity. In this paper, we give a complete description of the Jordan automorphisms of Tn+1(R), proving that every Jordan automorphism of Tn+1(R) can be written in a unique way as a product of a graph automorphism, an inner automorphism and a diagonal automorphism for n ≥ 1.

Keywords

17C3017C5013C10
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 52 , Issue 3 , September 2010 , pp. 529 - 536
Copyright
Copyright © Glasgow Mathematical Journal Trust 2010

References

REFERENCES

1.Ancochea, G., On semi-automorphisms of division algebra, Ann. Math. 48 (1947), 147–153.CrossRefGoogle Scholar
2.Baxter, W. E. and Martindale, W. S. III, Jordan homorphisms of semiprime rings, J. Algebra 56 (1979), 457–471.CrossRefGoogle Scholar
3.Beidar, K. I., Brešar, M. and Chebotar, M. A., Jordan isomorphisms of triangular matrix algebra over a connected commutative ring, Linear Algebra Appl. 312 (2000), 197–201.CrossRefGoogle Scholar
4.Brešar, M., Jordan mappings of semiprime rings, J. Algebra 127 (1989), 218–228.CrossRefGoogle Scholar
5.Cao, Y. A., Automorphisms of certain Lie algebras of upper triangular matrices over a commutative ring, J. Algebra 189 (1997), 506–513.CrossRefGoogle Scholar
6.Cao, Y. A., Automorphisms of the Lie algebras of strictly upper triangular matrices over certain commutative rings, Linear Algebra Appl. 329 (2001), 175–187.CrossRefGoogle Scholar
7.Herstein, L. N., Jordan automorphisms, Trans. Amer. Math. Soc. 81 (1956), 331–351.CrossRefGoogle Scholar
8.Jøndrup, S., Automorphisms of upper triangluar matrix rings, Arch Math. 49 (1987), 497–502.CrossRefGoogle Scholar
9.Kuzucuoglu, F. and Levchuk, V. M., The automorphisms groups of certain radical matrix rings, J. Algebra 243 (2001), 473–485.CrossRefGoogle Scholar
10.Tang, X. M., Cao, C. G. and Zhang, X., Modular automorphisms preserving idempotence and Jordan isomorphisms of triangular matrices over commutative rings, Linear Algebra Appl. 338 (2001), 145–152.Google Scholar
11.Wang, X. T., Decomposition of Jordan automorphisms of strictly upper triangular matrix algebra over commutative rings, Commut. Algebra 35 (2007), 1133–1140.CrossRefGoogle Scholar
12.Wang, X. T. and You, H., Decomposition of Jordan automorphisms of strictly triangular matrix algebra over local rings, Linear Algebra Appl. 392 (2004), 183–193.CrossRefGoogle Scholar
13.Wang, X. T. and You, H., Decomposition of Lie automorphisms of upper triangular matrix algebra over commutative rings, Linear Algebra Appl. 419 (2006), 466–474.CrossRefGoogle Scholar