Trace ideals of semidualizing modules and two generalizations of nearly Gorenstein rings

Abstract

In this article, we study the trace ideal of semidualizing modules. Also, we introduce two new classes of rings, namely quasi nearly Gorenstein and weakly nearly Gorenstein, which are generalizations of nearly Gorenstein rings. Furthermore, we show that the trace ideal of a semidualizing module is annihilators of certain Ext modules. Moreover, we give new versions of Tachikawa conjecture using quasi and weakly nearly Gorenstein rings.