New criteria for a ring to have a semisimple left quotient ring

摘要

Goldie's Theorem (1960), which is one of the most important results in Ring Theory, is a criterion for a ring to have a semisimple left quotient ring. The aim of the paper is to give four new criteria (using a completely different approach and new ideas). The first one is based on the recent fact that for an arbitrary ring R the set M of maximal left denominator sets of R is a non-empty set [V. V. Bavula, The largest left quotient ring of a ring, preprint (2011), arXiv:math.RA:1101.5107]: