Central and semicentral idempotents (Q2718038)
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scientific article; zbMATH DE number 1606254
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Central and semicentral idempotents |
scientific article; zbMATH DE number 1606254 |
Statements
5 June 2002
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rings with involutions
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left semicentral idempotents
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quasi-multiplications
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Central and semicentral idempotents (English)
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The authors prove some elementary properties of left semicentral idempotents. They prove that an idempotent \(e\) in a ring \(R\) is left (resp. right) semicentral if and only if \(e\) is right (resp. left) semicentral in the monoid \((R,\circ)\) where \(\circ\) is the quasi-multiplication in \(R\). They also prove that if \(R\) is a ring with an involution, an idempotent \(e\) in \(R\) is left (resp. right) semicentral if and only if \(e^*\) is right (resp. left) semicentral.
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