On universal localization of Morita equivalent rings

For a semiprime (left) Goldie ideal [Formula: see text] of the ring [Formula: see text], we determine the universal localization of the matrix ring [Formula: see text] at the ideal [Formula: see text]. As a corollary, we obtain a similar result for Goldie’s localization of [Formula: see text] at [Formula: see text]. We show that if [Formula: see text] is left Noetherian and [Formula: see text] is the prime radical of [Formula: see text], then the universal localization at [Formula: see text] respects Morita invariance. We present evidence to support our conjecture that this is true in general.