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In this paper, we introduce the concepts of 2-irreducible and strongly 2-irreducible ideals which are generalizations of irreducible and strongly irreducible ideals, respectively. We say that a proper ideal I of a ring R is 2-irreducible if for each ideals J, K and L of R, I= J\\cap K\\cap L implies that either I=J\\cap K "},"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":"1501.05243","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-01-21T17:40:53Z","cross_cats_sorted":[],"title_canon_sha256":"a22fa5029c386ed9aa4cbd2746cf89ff63a0add96783f8791f29b72370234b4a","abstract_canon_sha256":"cf66819bea15e3eea6ab630a343f91a5950beba6e82f3906fde2d3359fff55a8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:28:55.679564Z","signature_b64":"vtQq7S3swFWyIv6yZL+5qzACX0P+0QF6XcF0T63XhB0bXxMi3rn2fBlVQNSb61/fDP9F+20IrCEK4o1q1NEUDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"76ca0361b080db64e9d67725bf9d8d34cc19024b9b5dcc004916d2e500d9f6fe","last_reissued_at":"2026-05-18T02:28:55.679175Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:28:55.679175Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"2-irreducible and strongly 2-irreducible ideals of commutative rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Ahmad Yousefian Darani, Hojjat Mostafanasab","submitted_at":"2015-01-21T17:40:53Z","abstract_excerpt":"An ideal I of a commutative ring R is said to be irreducible if it cannot be written as the intersection of two larger ideals. 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