FP—内射环和IF环的几个特征

Some Characterizations of FP-injective Rings and IF Rings

中文摘要:

      本文给出了FP—内射环和IF环的如下几个特征:(l)R为右FP—内射环当且仅当任意左R—模正合列Kⁿ→Kⁿ→N→0 N为无挠模,当且仅当任一n阶矩阵环为右P—内射环;(2)R为左IF环当且仅当任一有限生成左R—模均可嵌入平坦模;(3)R为IF环当且仅当R为伪凝聚的上平坦环。

英文摘要:

      In this paper, we give some characterizations of right FP-injective rings and IF rings. For example, (1) R is a right FP-injective ring iff ecery left R- module exact sequence:Kⁿ→Kⁿ→N→0, where N is torsionless module, iff M_n(R) is right P-injective ring, for each natural number n. (2) R is left IF ring iff every finitely generated left R-module is embeddable in a flat module. (3) R is IF ring iff R is pseudo-coherent and coflat ring.