Relative regularity and Fredholm theory in semi-prime algebras with identity (Q797664)
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scientific article; zbMATH DE number 3867524
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Relative regularity and Fredholm theory in semi-prime algebras with identity |
scientific article; zbMATH DE number 3867524 |
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Relative regularity and Fredholm theory in semi-prime algebras with identity (English)
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1983
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Let A be a semiprime ring with unit. A left ideal is called of finite order, if it is generated by finitely many minimal idempotents. Main result of the paper is the statement that an element \(a\in A\) is invertible modulo the socle of A if and only if the ideals \(\{x\in A;\quad xa=0\}\) and \(\{x\in A;\quad ax=0\}\) are of finite order.
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ideals of finite order
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semiprime ring
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minimal idempotents
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