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arXiv · 2603.20202

On monoid graded semihereditary rings

Haneen Falah Ghalib Al-Kharsan·Parviz Sahandi·Nematollah Shirmohammadi
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Abstract

In order to study graded left hereditary and left semihereditary rings graded by a cancelation monoid in terms of their modules, we need to revisit graded free, projective, injective, and flat modules and provide graded versions of specific results concerning these modules, like Baer's criterion on injectivity and Lazard's theorem on flatness. Then, among other things, we can give some characterization of graded left hereditary and left semihereditary rings, in particular, of graded-Pr\"{u}fer and graded-Dedekind domains.

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Haneen Falah Ghalib Al-Kharsan, Parviz Sahandi, Nematollah Shirmohammadi. 2026-02-24. On monoid graded semihereditary rings. https://arxiv.org/abs/2603.20202

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