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arXiv · 2605.08095

A characterization of monoid graded semihereditary rings

Parviz Sahandi·Nematollah Shirmohammadi
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Abstract

Let $\Gamma$ be a cancellation monoid and $R=\bigoplus_{\alpha \in \Gamma}R_{\alpha}$ be a $\Gamma$-graded ring. It is shown that $R$ is graded left semihereditary if and only if $R$ is graded left coherent and every graded submodule of a flat left $R$-module is flat. Hence it gives a new characterization of graded-Pr\"{u}fer domains.

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Parviz Sahandi, Nematollah Shirmohammadi. 2026-04-12. A characterization of monoid graded semihereditary rings. https://arxiv.org/abs/2605.08095

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