Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9493331 | Journal of Algebra | 2005 | 24 Pages |
Abstract
If I is an ideal of a ring R, we say that idempotents lift strongly modulo I if, whenever a2âaâI, there exists e2=eâaR (equivalently e2=eâRa) such that eâaâI. The higher socles of R all enjoy this property, as does the Jacobson radical J if idempotents lift modulo J. Many of the useful, basic properties of lifting modulo J are shown to extend to any ideal I with strong lifting, and analogs of the semiperfect and semiregular rings are studied. A number of examples are given that limit possible extensions of the results.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
W.K. Nicholson, Y. Zhou,