{"paper":{"title":"Symbolic powers and generalized-parametric decomposition of monomial ideals on regular sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Adeleh Azari, Reza Naghipour, Simin Mollamahmoudi","submitted_at":"2018-11-16T15:53:56Z","abstract_excerpt":"Let $R$ be a commutative Noetherian ring and let ${\\bf x} :=x_1,\\ldots,x_d$ be a regular $R$-sequence contained in the Jacobson radical of $R$. An ideal $I$ of $R$ is said to be a monomial ideal with respect to ${\\bf x}$ if it is generated by a set of monomials $x_1^{e_1}\\ldots x_d^{e_d}$. It is shown that, if ${\\bf x}R$ is a prime ideal of $R$, then each monomial ideal $I$ has a canonical and unique decomposition as an irredundant finite intersection of primary ideals of the form $x^{e_1}_{\\tau(1)}R+\\dots+x^{e_s}_{\\tau(s)}R$, where $\\tau$ is a permutation of $\\{1,\\ldots,d\\}$, $s\\in\\{1,\\ldots,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.06881","kind":"arxiv","version":1},"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"}