(m,n)-内射和(m,n)-平坦函子

(m,n)-injective and(m,n)-flat functors

设R是有单位元的结合环,m和n是两个固定的正整数.引入了(m,n)-内射函子和(m,n)-平坦函子的概念,研究了这两类函子的一些性质,利用(m,n)-内射函子和(m,n)-平坦函子给出了(m,n)-凝聚环和Von Neumann正则环的一些等价刻画.

Let R be an associative ring with identity,m and n be fixed positive integers.The notions of(m,n)-injective functors and(m,n)-flat functors are introduced.Some properties of these two classes of functors are studied and some equivalent characterizations for(m,n)-coherent rings and Von Neumann regular rings are given in terms of(m,n)-injective functors and(m,n)-flat functors.