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SBI ring 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" . ==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.
抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)』 ■ウィキペディアで「SBI ring」の詳細全文を読む
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