In algebra, an SBI ring is a type of 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".
Definition
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 is not SBI.
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