I-n-Coherent Rings, I-n-Semihereditary Rings, and I-Regular Rings

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.