Geodesic
Galois extensions of radical algebras
Sbornik. Mathematics, Tome 30 (1976) no. 4, pp. 441-447 Cet article a éte moissonné depuis la source Math-Net.Ru

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Suppose $G$ is a finite group of automorphisms of an associative algebra $K$ with an identity element over a field $F$. Let $t(x)=\sum_{g\in G}x^g$. Assume that $\rho$ is a supernilpotent radical which is closed under the taking of subalgebras and satisfies the following condition: if $A\in\rho$ and $M$ is a nonempty set, then the ring $A_M$ of $M\times M$ matrices all but a finite number of whose columns are zero is radical. THEOREM. If $R$ is a two-sided ideal of $K$ and $K=t(K)K,$ then $t(R)\in\rho$ implies $R\in\rho$. Examples of radicals satisfying the above conditions are Baer's lower radical, the locally nilpotent radical, the locally finite radical, and also the algebraic kernel and Köthe radical, if $F$ is uncountable. Bibliography: 5 titles. 
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     author = {V. K. Kharchenko},
     title = {Galois extensions of radical algebras},
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     volume = {30},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1976_30_4_a1/}
}
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V. K. Kharchenko. Galois extensions of radical algebras. Sbornik. Mathematics, Tome 30 (1976) no. 4, pp. 441-447. http://geodesic.mathdoc.fr/item/SM_1976_30_4_a1/

[1] S. A. Amitsur, “A general theory of radical, II”, Amer. J. Math., 76:2 (1954), 100–120 | DOI | MR

[2] K. I. Beidar, “Koltso invariantov pri deistvii konechnoi gruppy avtomorfizmov koltsa”, Vsesoyuznyi algebraicheskii simpozium, Gomel, 1975, 279

[3] V. P. Elizarov, “Silnye predkrucheniya i silnye filtry, moduli i koltsa chastnykh”, Sib. matem. zh., 14:3 (1973), 549–559 | MR | Zbl

[4] V. K. Kharchenko, “Obobschennye tozhdestva s avtomorfizmami”, Algebra i logika, 14:2 (1975), 215–237 | MR | Zbl

[5] A. I. Shirshov, “O koltsakh s tozhdestvennymi sootnosheniyami”, Matem. sb., 43(85) (1957), 277–283 | Zbl