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We characterize the sequentially Cohen--Macaulayness of $L\\tensor_KN$ with respect to $Q$ as an $S$-module when $L$ and $N$ are non-zero finitely generated graded modules over $K[x_1, \\dots, x_m]$ and $K[y_1, \\dots, y_n]$, respectively. All hypersurface rings that are sequentially Cohen--Macaulay with respect to $Q$ are classified."},"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":"1112.3717","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-12-16T06:08:33Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"89785a8734cc4e9c4fcbffe3e76876412f6f20a6a264e59547434a450e9e8236","abstract_canon_sha256":"0c1ca14c26f3d1d414123b54746c132b870c006f60b9f0b0eb35d2f582466dd4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:30:15.896373Z","signature_b64":"8Y3IhCVEurpiXPB8IpE87fP+M3bRi8hj82cQAXmqmoiOUEax8jvn+NZ4Jw1sVTq/F1Xn4OxQOiIyKCkZETkjCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"35ee17606f89ca1b43117d49d652e7e7ea01477e56a106a1a42451cf50780fb3","last_reissued_at":"2026-05-18T01:30:15.895518Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:30:15.895518Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sequentially Cohen--Macaulayness of bigraded modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Ahad Rahimi","submitted_at":"2011-12-16T06:08:33Z","abstract_excerpt":"Let $K$ be a field, $S=K[x_1,\\ldots,x_m, y_1,\\ldots,y_n]$ be a standard bigraded polynomial ring and $M$ a finitely generated bigraded $S$-module. In this paper we study sequentially Cohen--Macaulayness of $M$ with respect to $Q=(y_1,\\ldots,y_n)$. We characterize the sequentially Cohen--Macaulayness of $L\\tensor_KN$ with respect to $Q$ as an $S$-module when $L$ and $N$ are non-zero finitely generated graded modules over $K[x_1, \\dots, x_m]$ and $K[y_1, \\dots, y_n]$, respectively. 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