Abstract:

 By means of comparison and analysis, some equivalent conditions of  the maximal right ideal as a module being a projective module were given firstly; then a new definition: MQ ring was introduced;  and the properties of MQ ring were discussed by max-injectivity and max\|flatness. Finally, the related properties of max-IF ring were summarized.

Key words: maxinjective module, maxflat module, MQ ring, maxIF ring