I-pure Submodules, I-FP-injective Modules and I-flat Modules
Zhanmin Zhu *
Department of Mathematics, Jiaxing University, Jiaxing, Zhejiang Province, 314001, P.R. China.
*Author to whom correspondence should be addressed.
Abstract
Let R be a ring and I an ideal of R. We define and study I-pure submodules , I-FP-injective modules, I-flat modules , I-coherent rings and I-semihereditary rings. Using the concepts of I-FP-injectivity and I-flatness of modules, we also present some characterizations of I-coherent rings and I-semihereditary rings.
Keywords: I-pure submodules, I-FP-injective modules, I-flat modules, I-coherent rings, I-semihereditary rings