Algebraic algebras with involution

Author:
Susan Montgomery

Journal:
Proc. Amer. Math. Soc. **31** (1972), 368-372

MathSciNet review:
0288149

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Abstract | References | Additional Information

Abstract: The following theorem is proved: Let be an algebra with involution over an uncountable field . Then if the symmetric elements of are algebraic, is algebraic.

**[1]**W. E. Baxter and W. S. Martindale III,*Rings with involution and polynomial identities*, Canad. J. Math.**20**(1968), 465–473. MR**0222116****[2]**I. N. Herstein and Susan Montgomery,*A note on division rings with involutions*, Michigan Math. J.**18**(1971), 75–79. MR**0283017****[3]**Nathan Jacobson,*Structure of rings*, American Mathematical Society Colloquium Publications, Vol. 37. Revised edition, American Mathematical Society, Providence, R.I., 1964. MR**0222106****[4]**Kevin McCrimmon,*On Herstein’s theorems relating Jordan and associative algebras*, J. Algebra**13**(1969), 382–392. MR**0249476****[5]**Susan Montgomery,*Polynomial identity algebras with involution*, Proc. Amer. Math. Soc.**27**(1971), 53–56. MR**0269695**, 10.1090/S0002-9939-1971-0269695-1**[6]**Susan Montgomery,*A generalization of a theorem of Jacobson*, Proc. Amer. Math. Soc.**28**(1971), 366–370. MR**0276272**, 10.1090/S0002-9939-1971-0276272-5**[7]**-, A generalization of a theorem of Jacobson. II (to appear).**[8]**J. Marshall Osborn,*Jordan and associative rings with nilpotent and invertible elements.*, J. Algebra**15**(1970), 301–308. MR**0262316**

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1972-0288149-0

Keywords:
Rings with involution,
algebraic algebras

Article copyright:
© Copyright 1972
American Mathematical Society