I−n-Coherent rings, I−n-semihereditary rings, and I-regular rings - Zhanmin, Zhu (Український математичний журнал, 2014)
Let R be a ring, let I be an ideal of R, and let n be a fixed positive integer. We define and study I−n-injective modules and I−n-flat modules. Moreover, we define and study left I−n-coherent rings, left I−n-semihereditary rings, and I-regular rings. By using the concepts of I−n-injectivity and I−n-flatness of modules, we also present some characterizations of the left I−n-coherent rings, left I−n-semihereditary rings, and I-regular rings.