Study of noncommutative Gorenstein rings

点击翻译按钮获取中文摘要

First, generalizing the notion of Gorenstein dimension for finitely generated modules over Noetherian rings, we introduced the notion of weak Gorenstein dimension for finitely presented modules over coherent rings. Next, we showed that for a coherent ring, if both the minimal cogenerator for left modules and that for right modules have finite flat dimension then they coincide, and that both the minimal cogenerator for left modules and that for right modules have finite flat dimension if and only if every finitely presented right module has a bounded weak Gorenstein dimension.