(9). Left quotients associative pairs and Morita invariant properties.

Autores: M. Gómez Lozano and M. Siles Molina. 

Revista:  Communications in Algebra. 32(7), (2004), 2841-2862.   (JCR: 117 de 180. Factor de impacto: 0.350)

Abstract: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) \lqp of an associative pair and show the existence of a maximal \lqp for every semiprime or left nonsingular associative pair. Moreover, we characterize those associative pairs for which their maximal \lqp is von Neumann regular and give a Gabriel-like characterization of associative pairs whose maximal \lqp is semiprime and artinian.