Mapping Galois extensions into division algebras

Vonessen, Nikolaus

doi:10.1090/S0002-9939-1993-1160306-4

Mapping Galois extensions into division algebras
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by Nikolaus Vonessen PDF

Proc. Amer. Math. Soc. 119 (1993), 1061-1068 Request permission

Abstract:

Let $A$ be a ring with a finite group of automorphisms $G$, and let ${f_1}$ and ${f_2}$ be homomorphisms from $A$ into some division algebra $D$ such that ${f_1}$ and ${f_2}$ agree on the fixed ring ${A^G}$. Assuming certain additional assumptions, it is shown that ${f_1}$ and ${f_2}$ differ only by an automorphism in $G$ and an inner automorphism of $D$.

References

Nicolas Bourbaki, Commutative algebra. Chapters 1–7, Elements of Mathematics (Berlin), Springer-Verlag, Berlin, 1989. Translated from the French; Reprint of the 1972 edition. MR 979760
J. C. McConnell and J. C. Robson, Noncommutative Noetherian rings, Pure and Applied Mathematics (New York), John Wiley & Sons, Ltd., Chichester, 1987. With the cooperation of L. W. Small; A Wiley-Interscience Publication. MR 934572
Susan Montgomery, Prime ideals in fixed rings, Comm. Algebra 9 (1981), no. 4, 423–449. MR 605031, DOI 10.1080/00927878108822591
Susan Montgomery, Prime ideals and group actions in noncommutative algebras, Invariant theory (Denton, TX, 1986) Contemp. Math., vol. 88, Amer. Math. Soc., Providence, RI, 1989, pp. 103–124. MR 999986, DOI 10.1090/conm/088/999986
Florian Pop and Horia Pop, An extension of the Noether-Skolem theorem, J. Pure Appl. Algebra 35 (1985), no. 3, 321–328. MR 777263, DOI 10.1016/0022-4049(85)90049-0