From Wikipedia, the free encyclopedia
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
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
-
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