SBI ring

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

This section needs expansion. You can help by adding missing information. (March 2026)

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.

Citations

References

• Jacobson, Nathan (1956), Structure of rings, American Mathematical Society, Colloquium Publications, vol. 37, Providence, R.I.: American Mathematical Society, ISBN 978-0-8218-1037-8, MR 0081264, Zbl 0073.02002 {{citation}}: ISBN / Date incompatibility (help)
• Kaplansky, Irving (1972), Fields and Rings, Chicago Lectures in Mathematics (2nd ed.), University Of Chicago Press, pp. 124–125, ISBN 0-226-42451-0, Zbl 1001.16500

This abstract algebra–related article is a stub. You can help Wikipedia by adding missing information.

• v
• t
• e