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We consider the following two questions: Describe the subsets $A \\subset \\mathbb{N}$ such that the set of polynomials $p_a$ with $a \\in A$ generate a prime ideal in S or the set of polynomials $p_a$ with $a \\in A$ is a regular sequence in S. We produce a large families of prime ideals by exploiting Serre's criterion for normality [4, Theorem 18.15] with the help of arithmetic considerations, vanishing sums of roots of unity [9]. We also deduce several other results concerning regular "},"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":"1309.1098","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-09-04T16:47:23Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"dd44d5376f12e011797c5c0457e55165d347380b4d304b95acc2f5ed3019bc16","abstract_canon_sha256":"fbd4d5635355f0dacb49ea4c09b97f7e54dd276761a143468a53bab27ada0858"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:14:09.099917Z","signature_b64":"RlxkVxGkwG+FF6cWTHzTUuEIkDkawPL9V2RGB37X1ufXGkeUaYCZdwetaOgtzrB71jkgnH1bZMrYSGWItRNWDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"503d314cfcc09cc569fd16f35d41b921f3bd3f7aff8baec143230bd3ffbb94fb","last_reissued_at":"2026-05-18T03:14:09.099253Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:14:09.099253Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Prime ideals and regular sequences of symmetric polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Neeraj Kumar","submitted_at":"2013-09-04T16:47:23Z","abstract_excerpt":"Let S=K[x_1,...,x_n] be a polynomial ring. Denote by $p_a$ the power sum symmetric polynomial x_1^a+...+x_n^a. We consider the following two questions: Describe the subsets $A \\subset \\mathbb{N}$ such that the set of polynomials $p_a$ with $a \\in A$ generate a prime ideal in S or the set of polynomials $p_a$ with $a \\in A$ is a regular sequence in S. We produce a large families of prime ideals by exploiting Serre's criterion for normality [4, Theorem 18.15] with the help of arithmetic considerations, vanishing sums of roots of unity [9]. 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