Article contents
Compressible matrix rings
Published online by Cambridge University Press: 17 April 2009
Abstract
Let Z(K) denote the center of a ring K. A ring R is compressible if Z(eRe) = eZ(R) for each idempotent e of R. In response to a question of S. Berberian, G. Bergman has constructed a (non-commutative) integral domain, satisfying a polynomial identity, for which the 2×2 matrix ring over the domain is not compressible. In contrast to Bergman's example, we show that the ring of nxn matrices over any commutative ring is always compressible.
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 30 , Issue 2 , October 1984 , pp. 295 - 298
- Copyright
- Copyright © Australian Mathematical Society 1984
References
REFERENCES
- 5
- Cited by