{"paper":{"title":"Characterizations of graded Pr\\\"ufer $\\star$-multiplication domains, II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Parviz Sahandi","submitted_at":"2016-10-16T12:01:56Z","abstract_excerpt":"Let $R=\\bigoplus_{\\alpha\\in\\Gamma}R_{\\alpha}$ be a graded integral domain and $\\star$ be a semistar operation on $R$. For $a\\in R$, denote by $C(a)$ the ideal of $R$ generated by homogeneous components of $a$ and for$f=f_0+f_1X+\\cdots+f_nX^n\\in R[X]$, let $\\A_f:=\\sum_{i=0}^nC(f_i)$. Let $N(\\star):=\\{f\\in R[X]\\mid f\\neq0\\text{and}\\A_f^{\\star}=R^{\\star}\\}$. In this paper we study relationships between ideal theoretic properties of $\\NA(R,\\star):=R[X]_{N(\\star)}$ and the homogeneous ideal theoretic properties of $R$. For example we show that $R$ is a graded Pr\\\"ufer-$\\star$-multiplication domain "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.04845","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"}