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This article is cited in 2 scientific papers (total in 2 papers)
Galois extensions of radical algebras
V. K. Kharchenko
Abstract:
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.
Received: 01.03.1976
Citation:
V. K. Kharchenko, “Galois extensions of radical algebras”, Math. USSR-Sb., 30:4 (1976), 441–447
Linking options:
https://www.mathnet.ru/eng/sm2909https://doi.org/10.1070/SM1976v030n04ABEH002282 https://www.mathnet.ru/eng/sm/v143/i4/p500
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Abstract page: | 357 | Russian version PDF: | 77 | English version PDF: | 15 | References: | 52 | First page: | 2 |
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