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The no-name lemma asserts that the invariant field of the quotient field of $K[L]$, $K(L)^G$ is a purely transcendental extension of $K^G$. In other words, there exist $y_1, \\ldots , y_n$ which are algebraically independent over $K^G$ such that $K(L)^G \\cong K^G(y_1, \\ldots , y_n)$. We define elements $\\lbrace y_1, \\ldots, y_n \\rbrace \\subset K[L]^G$ with the desired"},"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":"1801.09629","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-01-29T17:10:16Z","cross_cats_sorted":[],"title_canon_sha256":"7fc498246aa4310b4858409b19e6ecd8ff81cc4cb3d753bce8711a8f30b7117b","abstract_canon_sha256":"afad3c624b69f94889cbf434c3d8b1c01a6efa2374b46b49e27933b8aa69ee6f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:56.858991Z","signature_b64":"vUPBPcpTC1+xhszCdI/Dki3JIUCtxdonBnj2vXfccn4f1UzsfFVyTV0pOf2Q49dO21ltpzv9cM99ARAoZiB6BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"36a2762e2cbc51e32fc0c6561eef84c0d069bf6e50ad8cca713c635d5624e3e6","last_reissued_at":"2026-05-18T00:24:56.858397Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:56.858397Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Algebraic Construction of Quasi-split Algebraic Tori","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Armin Jamshidpey, Eric Schost, Nicole Lemire","submitted_at":"2018-01-29T17:10:16Z","abstract_excerpt":"The main purpose of this work is to give a constructive proof for a particular case of the no-name lemma. Let $G$ be a finite group, $K$ be a field, $L$ be a permutation $G$-lattice and $K[L]$ be the group algebra of $L$ over $K$. The no-name lemma asserts that the invariant field of the quotient field of $K[L]$, $K(L)^G$ is a purely transcendental extension of $K^G$. In other words, there exist $y_1, \\ldots , y_n$ which are algebraically independent over $K^G$ such that $K(L)^G \\cong K^G(y_1, \\ldots , y_n)$. 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