GI_(ac)-内射模与GI_(ac)-平坦模的环刻画

Ring characterizations on GI_(ac)-injective and GI_(ac)-flat modules

引入GI_(ac)-内射模和GI_(ac)-平坦模的概念,是介于GI-内射模(或GI-平坦模)与余纯内射模(或余纯平坦模)之间的一种模类.用上述模刻画了诸多环类,如:半单环、von Neumann正则环、遗传环和半遗传环.

The concept of GI_(ac)-injective modules and GI_(ac)-flat modules,is introduced respectively,which is a class of modules between GI-injective modules(or GI-flat modules)and copure injective modules(or copure flat modules).Some classes of rings,such as semisimple rings,von Neumann regular rings,hereditary rings and semihereditary rings,are characterized in terms of these modules.