On monoid graded semihereditary rings
Rings and Algebras
2026-04-21 v3 Commutative Algebra
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.
Keywords
Cite
@article{arxiv.2603.20202,
title = {On monoid graded semihereditary rings},
author = {Haneen Falah Ghalib Al-Kharsan and Parviz Sahandi and Nematollah Shirmohammadi},
journal= {arXiv preprint arXiv:2603.20202},
year = {2026}
}
Comments
Final version, 22 pages