On a generalization of Azumaya's exact rings (Q1891697)
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scientific article; zbMATH DE number 763907
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a generalization of Azumaya's exact rings |
scientific article; zbMATH DE number 763907 |
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On a generalization of Azumaya's exact rings (English)
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20 February 1996
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The notion of exact (artinian) rings introduced by Azumaya can be extended in a very natural way to bimodules. Basic properties of exact artinian rings are carried over to the general situation in Sections 1 and 2. The close relations of exact rings with locally distributive rings, duo rings, noetherian rings as well as with Morita (self-) duality are also discussed in this paper. The author proves that linearly compact duo rings are selfdual if the radical is a direct sum of colocal ideals.
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exact Artinian rings
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locally distributive rings
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duo rings
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Noetherian rings
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linearly compact duo rings
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radicals
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direct sums
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colocal ideals
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