Left quotient associative pairs and Morita invariant properties.
In this paper we prove that left nonsingularity and left
nonsingularity plus finite left local Goldie dimension are two Morita
invariant properties for idempotent rings
without total left or right zero divisors. Moreover, two Morita
equivalent idempotent rings, semiprime and left local
Goldie, have Fountain-Gould left quotient rings that are Morita
equivalent too. These results can be obtained from
others concerning associative pairs. We introduce the notion of (general)
left quotients pairs of an associative pair and show the
existence of a maximal left quotients pair for every semiprime or left
nonsingular associative pair. Moreover, we characterize those
associative pairs for which their maximal left quotients pairs is von
Neumann regular and give a Gabriel-like characterization of
associative pairs whose maximal left quotients pairs is semiprime and
artinian.
(This paper has appeared in Comm. Algebra 32
(2004), no. 7, 2841--2862)
M. Gómez Lozano < magomez@agt.cie.uma.es >
M. Siles Molina. < mercedes@agt.cie.uma.es. >