A characterization of monoid graded semihereditary rings

Abstract

Let $\hat{I}“$ be a cancellation monoid and $R={⨁}_{\hat{I}\pm \in \hat{I}“}{R}_{\hat{I}}\pm$ be a $\hat{I}“$-graded ring. It is shown that $R$ is graded left semihereditary if and only if $R$ is graded left coherent and every graded submodule of a flat left $R$-module is flat. Hence it gives a new characterization of graded-Prüfer domains.

7 pages