Topological Jacobson radicals. III (Q6597856)
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scientific article; zbMATH DE number 7906276
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Topological Jacobson radicals. III |
scientific article; zbMATH DE number 7906276 |
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Topological Jacobson radicals. III (English)
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4 September 2024
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The main results of the paper find sufficient conditions under which a radical (with or without some extra properties) is defined on some (subclass of a) class of (topological) algebras.\N\NThe studied class is a variety of \(F\)-algebras in the Chapter 2, class of topological algebras over certain topological ring in the Chapter 3 and a variety of topological algebras over certain topological ring in the Chapter 4.\N\NIn addition to the results about the radicals, many other results are obtained concerning, for example, topological quasi-regularity, topological invertibility and other properties of elements and subsets.\N\NAs the final result, a version of Nakayama's lemma for topological algebras is stated.
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radical defined on variety
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radical defined on a class of topological algebras
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Jacobson radical
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topological Jacobson radical
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F-algebras
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irreducible modules
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irreducible topological modules
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topological quasi-regularity
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topological invertibility
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\(\Sigma\)-solvability of ideals
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Nakayama's lemma
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