On TR- rings and STF-rings

Abstract

A ring R is said to be TR- rings , if for all and is called right (left) SF-ring , if every simple right (left) -module is -flat . In this paper , we give some characterization of - rings and S F-rings . Further , it is shown that is - ring if and only if , is S F-ring , with for every if and only if is with every essential right ideal is -flat . Additionally , we have investigated - rings with simple singular right - modules are -flat .