A NEW DUALITY THEOREM FOR SEMISIMPLE MODULES AND CHARACTERIZATION OF VILLAMAYOR RINGS

We prove the theorem: If R is a ring whose right ideals satisfy the do uble annihilator condition with respect to a semisimple right R-module W, then every right ideal is an intersection of maximal right ideals, consequently R is a right V (for Villamayor) ring, and W is then nece ssarily a cogenerator of mod-R. (The converse is well known.) We use t his to give a new proof of a theorem of ours on right Johns rings.