In this paper, it is shown that for a QF ring R, the category of projectiveleft R-modules is a category with factorization if and only if gl.dim R ≤1, moreover, ifP(RR) = P(RR) = O,then the meta-Grothendieck groups o...In this paper, it is shown that for a QF ring R, the category of projectiveleft R-modules is a category with factorization if and only if gl.dim R ≤1, moreover, ifP(RR) = P(RR) = O,then the meta-Grothendieck groups obtained by left modules orby right modules are the same, up to isomorphism. It is also shown that the category of f.g. meta-pojective left R-modules is not only a category with factorization but also acategory with product such that it has a small skeletal subcategory.展开更多
基金Supported by the National Natural Science Foundation of China(1990100),theNatural Science Foundation of Guangdong Province.
文摘In this paper, it is shown that for a QF ring R, the category of projectiveleft R-modules is a category with factorization if and only if gl.dim R ≤1, moreover, ifP(RR) = P(RR) = O,then the meta-Grothendieck groups obtained by left modules orby right modules are the same, up to isomorphism. It is also shown that the category of f.g. meta-pojective left R-modules is not only a category with factorization but also acategory with product such that it has a small skeletal subcategory.
