SBI ring
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In 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" (Jacobson 1956, p.53).
Examples
- Any ring with nil radical is SBI.
- Any Banach algebra is SBI: more generally, so is any compact topological ring.
- The ring of rational numbers with odd denominator, and more generally, any local ring, is SBI.
References
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