{"paper":{"title":"Modules Satisfying the Prime Radical Condition and a Sheaf Construction for Modules II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.RA"],"primary_cat":"math.AC","authors_text":"Mahmood Behboodi, Mansour Aghasi, Masoud Sabzevari","submitted_at":"2012-02-02T08:25:05Z","abstract_excerpt":"In this paper we continue our study of modules satisfying the prime radical condition ($\\mathbb{P}$-radical modules), that was introduced in Part I (see \\cite{BS}). Let $R$ be a commutative ring with identity. The purpose of this paper is to show that the theory of spectrum of $\\mathbb{P}$-radical $R$-modules (with the Zariski topology) resembles to that of rings. First, we investigate the behavior of $\\mathbb{P}$-radical modules under localization and direct sums. Finally, we describe the construction of a structure sheaf on the prime spectrum Spec$(M)$, which generalizes the classical struct"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.0381","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"}