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The former are important in the study of modules over Gorenstein rings, while the latter arise in a natural way from generic formal fibers and derivations.\n  We characterize one-dimensional stable local rings in several ways. The characterizations involve th"},"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":"1603.02173","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-03-07T17:47:28Z","cross_cats_sorted":[],"title_canon_sha256":"25c512326a43ca40cfb3e8e0c1c1a2fb41cfb58c092323a26ab01766cfbb8d9e","abstract_canon_sha256":"da50a201b4f8c364dba60936f0c88e86fea1dba8768a9b08d104cc2dc9904993"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:31.451578Z","signature_b64":"wv18XLDF9Rx/YJwtkAPEtM3HOvbuVlzq3ORlZtbapsYtS2/8mo9ykQBPg3y9ICTr7D6vZCaIlNOM1PAtttEVDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0243a4cf91ede93ae7371926602c948f32e42fd81fe0fb1f6da613e5dd36bc0c","last_reissued_at":"2026-05-18T01:19:31.450833Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:31.450833Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"One-dimensional stable rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Bruce Olberding","submitted_at":"2016-03-07T17:47:28Z","abstract_excerpt":"A commutative ring $R$ is stable provided every ideal of $R$ containing a nonzerodivisor is projective as a module over its ring of endomorphisms. 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