Chain conditions for modular right ideals and right adjoint ideals. (Q1769433)
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scientific article; zbMATH DE number 2148373
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Chain conditions for modular right ideals and right adjoint ideals. |
scientific article; zbMATH DE number 2148373 |
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Chain conditions for modular right ideals and right adjoint ideals. (English)
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21 March 2005
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The relations between right adjoint ideals and modular right ideals are investigated. It is proved that in a right Artinian ring every chain of modular right ideals is finite and any two maximal chains have the same length. A semiprime ring with dcc for right adjoint ideals and left adjoint ideals is characterized as a direct sum of a semisimple Artinian ring with a Jacobson radical ring.
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chain conditions
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circle condition
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adjoint ideals
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modular right ideals
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right Artinian rings
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semiprime rings
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direct sums
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semisimple Artinian rings
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Jacobson radical rings
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