{"paper":{"title":"Coherence of the ring of periodic distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.GN","math.RA"],"primary_cat":"math.FA","authors_text":"Amol Sasane","submitted_at":"2016-06-15T09:04:41Z","abstract_excerpt":"It is shown that the ring of periodic distributions is a coherent ring (with the operations of pointwise addition and convolution) by showing that the isomorphic ring $s'$ of the Fourier coefficients (of sequences of at most polynomial growth) with termwise operations is coherent. Moreover, it is shown that the subring $\\ell^\\infty$ of $s'$ of all bounded sequences is coherent too, while the subring $c$ of $\\ell^\\infty$ of all convergent sequences is not coherent. It is also observed that $s'$ is a Hermite ring, but not a projective free ring."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.04685","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}