{"paper":{"title":"Characterizations of graded Pr\\\"ufer $\\star$-multiplication domains","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Parviz Sahandi","submitted_at":"2013-07-15T09:24:38Z","abstract_excerpt":"Let $R=\\bigoplus_{\\alpha\\in\\Gamma}R_{\\alpha}$ be a graded integral domain graded by an arbitrary grading torsionless monoid $\\Gamma$, and $\\star$ be a semistar operation on $R$. In this paper we define and study the graded integral domain analogue of $\\star$-Nagata and Kronecker function rings of $R$ with respect to $\\star$. We say that $R$ is a graded Pr\\\"{u}fer $\\star$-multiplication domain if each nonzero finitely generated homogeneous ideal of $R$ is $\\star_f$-invertible. Using $\\star$-Nagata and Kronecker function rings, we give several different equivalent conditions for $R$ to be a grad"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.3861","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}