Geodesic
Invariant Subgroups in Rings with Involution
Canadian journal of mathematics, Tome 30 (1978) no. 2, pp. 350-357

Voir la notice de l'article provenant de la source Cambridge University Press

Let R be a ring with involution*. In this paper, we study additive subgroups A of R which are invariant under all mappings of the form φx : a → xax*. That is, xAx* ⊆ A for all x ∈ R. Obvious examples of such subgroups A are ideals of R, the set of symmetric elements, and the set of skew-symmetric elements. We will prove that when R is *-prime, these examples are essentially the only ones. 
Montgomery, Susan. Invariant Subgroups in Rings with Involution. Canadian journal of mathematics, Tome 30 (1978) no. 2, pp. 350-357. doi: 10.4153/CJM-1978-031-x
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[1] 1. Bass, H., Unitary algebraic K-theory, Lecture Notes in Mathematics 3^3 (Springer-Verlag, Berlin, 1973). Google Scholar

[2] 2. Baxter, W. E., A condition of Brauer-Cartan-Hua type (to appear). Google Scholar

[3] 3. Erickson, T. S., The Lie Structure in prime rings with involution, J. Algebra 21 (1972), 523–534. Google Scholar

[4] 4. Herstein, I.N., On a theorem of Brauer-Cartan-Hua type. Pacific J. Math. 57 (1975), 177–181. Google Scholar

[5] 5. Herstein, I.N. Rings with involution (University of Chicago Press, Chicago, 1976). Google Scholar

[6] 6. Lee, P. H., On subrings of rings with involution, Pacific J. Math. 60 (1975), 131–147. Google Scholar

[7] 7. Martindale, W. S. III, Prime rings satisfying a generalized polynomial identity, J. Algebra 12 (1969), 576–584. Google Scholar

[8] 8. McCrimmon, K., On Herstein s theorems relating Jordan and associative algebras, J. Algebra 13 (1969), 382–392. Google Scholar

[9] 9. Rowen, L. H., Structure of rings with involution applied to generalized polynomial identities, Can. J. Math. 27 (1975), 573–584. Google Scholar

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