%0 Journal Article %T Gorenstein hereditary rings with respect to a semidualizing module %J Bulletin of the Iranian Mathematical Society %I Iranian Mathematical Society (IMS) %Z 1017-060X %A Zhao, G. %A Zhang, B. %D 2017 %\ 11/30/2017 %V 43 %N 6 %P 1671-1677 %! Gorenstein hereditary rings with respect to a semidualizing module %K Semidualizing module‎ %K ‎$G_C$-projective module‎ %K ‎$G_C$-flat module‎ %K ‎$G_C$-(semi)hereditary ring‎ %K ‎coherent ring‎ %R %X ‎Let $C$ be a semidualizing module‎. ‎We first investigate the properties of‎ ‎finitely generated $G_C$-projective modules‎. ‎Then‎, ‎relative to $C$‎, ‎we introduce and study the rings over which‎ ‎every submodule of a projective (flat) module is $G_C$-projective (flat)‎, ‎which we call $C$-Gorenstein (semi)hereditary rings‎. ‎It is proved that every $C$-Gorenstein hereditary ring is both coherent and $C$-Gorenstein semihereditary. %U http://bims.iranjournals.ir/article_1052_a5c3f63a6c7c776ea5aa5f168bb1c109.pdf