Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Jordan isomorphisms of triangular rings


Author: Tsai-Lien Wong
Journal: Proc. Amer. Math. Soc. 133 (2005), 3381-3388
MSC (2000): Primary 47L35; Secondary 16S50
DOI: https://doi.org/10.1090/S0002-9939-05-07989-X
Published electronically: June 7, 2005
MathSciNet review: 2161163
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We investigate Jordan isomorphisms of triangular rings and give a sufficient condition under which they are necessarily isomorphisms or anti-isomorphisms. As corollaries we obtain generalizations of two recent results: the one concerning Jordan isomorphisms of triangular matrix algebras by Beidar, Bresar and Chebotar, and the one concerning Jordan isomorphisms of nest algebras by Lu.


References [Enhancements On Off] (What's this?)

  • 1. G. Ancochea, Le théorème de von Staundt en géometrie projective quaternionienne, J. Reine Angew. Math. 184 (1942), 192-198. MR 0008893 (5:72d)
  • 2. G. Ancochea, On semi-automorphisms of division algebras, Ann. Math. 48 (1947), 147-153. MR 0018642 (8:310c)
  • 3. W.E. Baxter and W.S. Martindale 3rd, Jordan homomorphisms of semiprime rings, J. Algebra 56 (1979), 457-471. MR 0528587 (80f:16008)
  • 4. K.I. Beidar, M. Bresar, M.A. Chebotar, Jordan isomorphisms of triangular matrix algebras over a connected commutative ring, Linear Algebra Appl. 312 (2000), 197-201. MR 1759333 (2001a:16048)
  • 5. M. Bresar, Jordan mappings of semiprime rings, J. Algebra 127 (1989), 218-228. MR 1029414 (91a:16025)
  • 6. M. Bresar, Jordan mappings of semiprime rings II, Bull. Austral. Math. Soc. 44 (1991), 233-238. MR 1126361 (92j:16024)
  • 7. W.-S. Cheung, Commuting maps of triangular algebras, J. London Math. Soc. 63 (2001), 117-127. MR 1802761 (2001k:16053)
  • 8. K.R. Davidson, Nest algebras, Pitman Research Notes in Mathematics, Vol. 191, Longman, London/New York, 1988. MR 0972978 (90f:47062)
  • 9. I.N. Herstein, Jordan homomorphisms, Trans. Amer. Math. Soc. 81 (1956), 331-351. MR 0076751 (17,938f)
  • 10. L.-K. Hua, On the automorphisms of a s-field, Proc. Nat. Acad. Sci. U.S.A. 35 (1949), 386-389. MR 0029886 (10:675d)
  • 11. N. Jacobson and C. Rickart, Jordan homomorphisms of rings, Trans. Amer. Math. Soc. 69 (1950), 479-502. MR 0038335 (12:387h)
  • 12. I. Kaplansky, Semi-automorphisms of rings, Duke Math. J. 14 (1947), 521-527. MR 0022209 (9:172e)
  • 13. F. Lu, Jordan isomorphisms of nest algebras, Proc. Amer. Math. Soc. 131 (2002), 147-154. MR 1929034 (2003f:47121)
  • 14. L. Molnár, P. Semrl, Some linear preserver problems on upper triangular matrices, Linear and Multilinear Algebra 45 (1998), 189-206.MR 1671619 (99h:15003)
  • 15. J.R. Ringrose, On some algebras of operators, Proc. London Math. Soc. 15 (1965), 61-83.MR 0171174 (30:1405)
  • 16. J.R. Ringrose, On some algebras of operators II, Proc. London Math. Soc. 16 (1966), 385-402.MR 0196516 (33:4703)
  • 17. M.F. Smiley, Jordan homomorphisms onto prime rings, Trans. Amer. Math. Soc. 84 (1957), 426-429. MR 0083484 (18:715b)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 47L35, 16S50

Retrieve articles in all journals with MSC (2000): 47L35, 16S50


Additional Information

Tsai-Lien Wong
Affiliation: Department of Applied Mathematics, National Sun Yat-Sen University, Kaohsiung, Taiwan, 804
Email: tlwong@math.nsysu.edu.tw

DOI: https://doi.org/10.1090/S0002-9939-05-07989-X
Keywords: Jordan isomorphisms, triangular rings, triangular matrix algebras, nest algebras
Received by editor(s): June 29, 2004
Published electronically: June 7, 2005
Additional Notes: This research was supported by NSC Grants NSC 91-2115-M-110-005
Communicated by: David R. Larson
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society