ON EXCHANGE RINGS WITH BOUNDED INDEX OF NILPOTENCE

Abstract

This paper studies exchange rings R such that R/J(R) has bounded index of nilpotence. We give several characterizations of such rings. We prove that if a semiprimitive exchange ring R has index n, then for any maximal two-sided I of R, if R/I has length n, then there exists a central idempotent element e in R such that eRe is an n by n full matrix ring over some exchange ring with central idempotents, and the restriction π from eRe to R/I is surjective.

Keywords:

• Exchange ring
• Index of nilpotence
• Semiperfect ring
• 1991 Mathematics Subject Classification: 16D60

ACKNOWLEDGMENTS

The author expresses his gratitude to the referee for his/her careful reading and suggestions which improved the exposition of the paper.