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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 "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1610.04845","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-10-16T12:01:56Z","cross_cats_sorted":[],"title_canon_sha256":"5608b33e290aca4ffe20199af2cbab5b15df57d7ae34834f2cb191e0dc628a56","abstract_canon_sha256":"ec1b617710a3110a9f311edd700bd649c5f4517ff44e811490a9aaccfa1839c7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:13.137187Z","signature_b64":"RBXt9PwNu1Hpa8bVMQPDb7joFD6GyVlL/Tskr7zr9/6Lx/FT2050VJSKtFLDLET2hsq94VdwSaKFJ73na+kSDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5d68f011665d985747628eb5ea2390b92a940118b6684543441eeb6ab2151be1","last_reissued_at":"2026-05-18T00:39:13.136495Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:13.136495Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $R$. 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