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)

 
 

 

Rings with involution all of whose symmetric elements are nilpotent or regular


Authors: J. Chacron and M. Chacron
Journal: Proc. Amer. Math. Soc. 37 (1973), 397-402
MSC: Primary 16A28
DOI: https://doi.org/10.1090/S0002-9939-1973-0320058-1
MathSciNet review: 0320058
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that noetherian rings with involution having all their symmetric elements nilpotent or regular are orders in artinian rings with involution having all their symmetric elements nilpotent or invertible.


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

  • [1] W. E. Baxter and W. S. Martindale III, Rings with involution and polynomial identities, Canad. J. Math. 20 (1968), 465-473. MR 36 #5168. MR 0222116 (36:5168)
  • [2] W. A. Goldie, The transfer ideal, Séminaire d'algèbre non commutative, Orsay, 1967/1968, Conf. 1.
  • [3] I. N. Herstein and S. Montgomery, Invertible and regular elements in rings with involution, J. Algebra (to appear). MR 0313301 (47:1856)
  • [4] I. N. Herstein, Topics in ring theory, Univ. of Chicago Press, Chicago, Ill., 1969. MR 42 #6018. MR 0271135 (42:6018)
  • [5] N. Jacobson, Structure of rings, rev. ed., Amer. Math. Soc. Colloq. Publ., vol. 37, Amer. Math. Soc., Providence, R.I., 1964. MR 36 #5158. MR 0222106 (36:5158)
  • [6] C. Lanski, Rings with involution whose symmetric elements are regular, Proc. Amer. Math. Soc. (to appear). MR 0292889 (45:1971)
  • [7] L. Lesieur, Anneaux noetheriens à gauche complètement primaires et anneaux co-irréductibles, J. Reine Angew. Math. 241 (1970), 106-117. MR 41 #3515. MR 0258870 (41:3515)
  • [8] K. McCrimmon, On Herstein's theorems relating Jordan and associative algebras, J. Algebra 13 (1969), 382-392. MR 40 #2721. MR 0249476 (40:2721)
  • [9] K. McCrimmon, Quadratic Jordan algebras whose elements are all invertible or nilpotent, Proc. Amer. Math. Soc. 35 (1972), 309-316. MR 0308217 (46:7332)
  • [10] S. Montgomery, Polynomial identity algebras with involution, Proc. Amer. Math. Soc. 27 (1971), 53-56. MR 42 #4590. MR 0269695 (42:4590)
  • [11] J. M. Osborn, Jordan algebras of capacity two, Proc. Nat. Acad. Sci. U.S.A. 57 (1967), 582-588. MR 35 #6727. MR 0215892 (35:6727)
  • [12] -, Jordan and associative rings with nilpotent and invertible elements, J. Algebra 15 (1970), 301-308. MR 41 #6925. MR 0262316 (41:6925)
  • [13] L. Small, Orders in Artinian rings, J. Algebra 4 (1966), 13-41. MR 34 #199. MR 0200300 (34:199)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 16A28

Retrieve articles in all journals with MSC: 16A28


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0320058-1
Keywords: Noetherian rings with involution, regular symmetric elements, nilpotent symmetric elements
Article copyright: © Copyright 1973 American Mathematical Society

American Mathematical Society