A generalization of a theorem of Jacobson
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- by Susan Montgomery PDF
- Proc. Amer. Math. Soc. 28 (1971), 366-370 Request permission
Abstract:
A well-known theorem of Jacobson asserts that a ring $R$ in which ${x^{n(x)}} = x$ for each $x$ in $R$ must be commutative. This paper gives a description of a ring with involution in which the above condition is imposed only on the symmetric elements. In particular, if $R$ is primitive, $R$ is either commutative or the $2 \times 2$ matrices over a field, and, in general, any such $R$ is locally finite and satisfies a polynomial identity of degree 8.References
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Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 28 (1971), 366-370
- MSC: Primary 16.58
- DOI: https://doi.org/10.1090/S0002-9939-1971-0276272-5
- MathSciNet review: 0276272