Morita Invariance and Maximal Left Quotient Rings

Abstract

We prove that under conditions of regularity the maximal left quotient ring of a corner of a ring is the corner of the maximal left quotient ring. We show that if R and S are two non-unital Morita equivalent rings then their maximal left quotient rings are not necessarily Morita equivalent. This situation contrasts with the unital case. However we prove that the ideals generated by two Morita equivalent idempotent rings inside their own maximal left quotient rings are Morita equivalent.

Key Words:

• Morita invariance
• Maximal left quotient ring
• Corner

1991 Mathematics Subject Classification:

• 16D90
• 16S90

Acknowledgments

This work is partially supported by the MCYT, BFM2001-1938-C02-01 and the “Plan Andaluz de Investigación y Desarrollo Tecnológico,” FQM 264; and, in particular, the first author is partially supported by a FPU grant by the MECD (AP2001-1368).

Notes

^#Communicated by J. Kuzmanovich.