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.
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 66, No. 6, pp. 767–786, June, 2014.
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Zhanmin, Z. I-n-Coherent Rings, I-n-Semihereditary Rings, and I-Regular Rings. Ukr Math J 66, 857–883 (2014). https://doi.org/10.1007/s11253-014-0978-8
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DOI: https://doi.org/10.1007/s11253-014-0978-8