A characterization of monoid graded semihereditary rings

Parviz Sahandi, Nematollah Shirmohammadi

Let $\Gamma$ be a cancellation monoid and $R={⨁}_{\alpha \in \Gamma }{R}_{\alpha }$ be a $\Gamma$-graded ring. It is shown that $R$ is graded left semihereditary if and only if $R$ is graded left coherent a…