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".[1]
Examples
[edit | edit source]- 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.
Citations
[edit | edit source]- ^ Jacobson (1956), p. 53
References
[edit | edit source]- Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value).
- Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value).
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