关键词: 循环纯, 循环纯phantom态射, 预覆盖

Abstract: By introducing the notion of cyclic pure phantom morphisms, we gave  some equivalent characterizations of cyclic pure phantom morphisms,  proved that every R-module had an epic cyclic pure phantom cover with the kernel cyclic pure injective modules, and discussed the transitivity of cyclic pure phantom precover under change of rings.

Key words: cyclic pure, cyclic pure phantom morphism, precover