{"paper":{"title":"Almost Gorenstein Rees algebras of $p_g$-ideals, good ideals, and powers of the maximal ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Ken-ichi Yoshida, Naoki Taniguchi, Naoyuki Matsuoka, Shiro Goto","submitted_at":"2016-07-20T09:57:47Z","abstract_excerpt":"Let $(A,{\\mathfrak m})$ be a Cohen-Macaulay local ring and let $I$ be an ideal of $A$. We prove that the Rees algebra ${\\mathcal R}(I)$ is an almost Gorenstein ring in the following cases: (1) $(A,{\\mathfrak m})$ is a two-dimensional excellent Gorenstein normal domain over an algebraically closed field $K \\cong A/{\\mathfrak m}$ and $I$ is a $p_g$-ideal; (2) $(A,{\\mathfrak m})$ is a two-dimensional almost Gorenstein local ring having minimal multiplicity and $I={\\mathfrak m}^{\\ell}$ for all $\\ell \\ge 1$; (3) $(A,{\\mathfrak m})$ is a regular local ring of dimension $d \\ge 2$ and $I={\\mathfrak m}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.05894","kind":"arxiv","version":3},"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"}