A Γ-graded ring is graded left semihereditary iff it is graded left coherent and graded submodules of flat modules are flat, giving a characterization of graded-Prüfer domains.
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A characterization of monoid graded semihereditary rings
A Γ-graded ring is graded left semihereditary iff it is graded left coherent and graded submodules of flat modules are flat, giving a characterization of graded-Prüfer domains.