SBI ring

 ( Ring Theory ) 

In abstract algebra, an SBI ring is a ring R (with identity) such that every idempotent of R modulo the Jacobson radical can be lifted to R. The abbreviation SBI was introduced by Irving Kaplansky and stands for "suitable for building idempotent elements".

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Examples

• Any ring with Nil ideal radical is SBI.
• Any Banach algebra is SBI: more generally, so is any Compact space topological ring.
• The ring of with odd denominator, and more generally, any local ring, is SBI.

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Citations

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