Graded analogs of Baer's criterion and Lazard's theorem characterize graded left hereditary and semihereditary rings over cancellation monoids.
Sahandi,Characterizations of graded Pr¨ ufer⋆-multiplication domains, II, Bull
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On monoid graded semihereditary rings
Graded analogs of Baer's criterion and Lazard's theorem characterize graded left hereditary and semihereditary rings over cancellation monoids.