{"paper":{"title":"On 2-absorbing ideals of commutative semirings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Hussein Behzadipour, Peyman Nasehpour","submitted_at":"2018-05-30T13:02:22Z","abstract_excerpt":"In this paper, we investigate 2-absorbing ideals of commutative semirings and prove that if $\\mathfrak{a}$ is a nonzero proper ideal of a subtractive valuation semiring $S$ then $\\mathfrak{a}$ is a 2-absorbing ideal of $S$ if and only if $\\mathfrak{a}=\\mathfrak{p}$ or $\\mathfrak{a}=\\mathfrak{p}^2$ where $\\mathfrak{p}=\\sqrt\\mathfrak{a}$ is a prime ideal of $S$. We also show that each 2-absorbing ideal of a subtractive semiring $S$ is prime if and only if the prime ideals of $S$ are comparable and if $\\mathfrak{p}$ is a minimal prime over a 2-absorbing ideal $\\mathfrak{a}$, then $\\mathfrak{am} ="},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.11928","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"}