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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} ="},"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":"1805.11928","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-05-30T13:02:22Z","cross_cats_sorted":[],"title_canon_sha256":"79577abef8d4a026ff3e3672449b6a6b76efec7f1f383fa1cb62aaa798508864","abstract_canon_sha256":"81f39073ed4d4597adcdfa967c13798b1e32bcc9c490589868882961ca37b8fd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:33.819808Z","signature_b64":"mw5Yhna2QfKc/WOY8lu6PmXviiXzpSAoBqouu17rvsCf8XIOWhoXPdbHEV9sGALlT3NDpQqfJL19MtG2fUNEBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"44c6f4bb28daaf369055e679f44dcee258929bb1f51c42ba6444afc158e72bf4","last_reissued_at":"2026-05-17T23:51:33.819200Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:33.819200Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $S$. 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