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

Chacron, J.; Chacron, M.

doi:10.1090/S0002-9939-1973-0320058-1

Rings with involution all of whose symmetric elements are nilpotent or regular
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by J. Chacron and M. Chacron PDF

Proc. Amer. Math. Soc. 37 (1973), 397-402 Request permission

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

W. E. Baxter and W. S. Martindale III, Rings with involution and polynomial identities, Canadian J. Math. 20 (1968), 465–473. MR 222116, DOI 10.4153/CJM-1968-043-6

The transfer ideal

I. N. Herstein and Susan Montgomery, Invertible and regular elements in rings with involution, J. Algebra 25 (1973), 390–400. MR 313301, DOI 10.1016/0021-8693(73)90052-5
I. N. Herstein, Topics in ring theory, University of Chicago Press, Chicago, Ill.-London, 1969. MR 0271135
Nathan Jacobson, Structure of rings, Revised edition, American Mathematical Society Colloquium Publications, Vol. 37, American Mathematical Society, Providence, R.I., 1964. MR 0222106
Charles Lanski, Rings with involution whose symmetric elements are regular, Proc. Amer. Math. Soc. 33 (1972), 264–270. MR 292889, DOI 10.1090/S0002-9939-1972-0292889-7
L. Lesieur, Anneaux noetheriens à gauche complètement primaires et anneaux co-irréductibles, J. Reine Angew. Math. 241 (1970), 106–117 (French). MR 258870, DOI 10.1515/crll.1970.241.106
Kevin McCrimmon, On Herstein’s theorems relating Jordan and associative algebras, J. Algebra 13 (1969), 382–392. MR 249476, DOI 10.1016/0021-8693(69)90081-7
Kevin McCrimmon, Quadratic Jordan algebras whose elements are all invertible or nilpotent, Proc. Amer. Math. Soc. 35 (1972), 309–316. MR 308217, DOI 10.1090/S0002-9939-1972-0308217-4
Susan Montgomery, Polynomial identity algebras with involution, Proc. Amer. Math. Soc. 27 (1971), 53–56. MR 269695, DOI 10.1090/S0002-9939-1971-0269695-1
J. Marshall Osborn, Jordan algebras of capacity two, Proc. Nat. Acad. Sci. U.S.A. 57 (1967), 582–588. MR 215892, DOI 10.1073/pnas.57.3.582
J. Marshall Osborn, Jordan and associative rings with nilpotent and invertible elements, J. Algebra 15 (1970), 301–308. MR 262316, DOI 10.1016/0021-8693(70)90058-X
Lance W. Small, Orders in Artinian rings, J. Algebra 4 (1966), 13–41. MR 200300, DOI 10.1016/0021-8693(66)90047-0