{"abstracts":[{"sha1":"ebf57628491a858778f7c95721ca2920e03a90bb","content":"Let I be a squarefree monomial ideal of a polynomial ring S. In this\npaper, we prove that the arithmetical rank of I is equal to the projective\ndimension of S/I when one of the following conditions is satisfied: (1) μ\n(I) ≤ 5; (2) I ≤ 4.","mimetype":"text/plain","lang":"en"},{"sha1":"abe4e56438a9c677f1a0288c54433cfc0f791d7f","content":"Let $I$ be a squarefree monomial ideal of a polynomial ring $S$. In this\npaper, we prove that the arithmetical rank of $I$ is equal to the projective\ndimension of $S/I$ when one of the following conditions is satisfied: (1) $\\mu\n(I) \\leq 5$; (2) $\\arithdeg I \\leq 4$.","mimetype":"application/x-latex","lang":"en"}],"refs":[],"contribs":[{"index":0,"raw_name":"Kyouko Kimura","role":"author"},{"index":1,"raw_name":"Giancarlo Rinaldo","role":"author"},{"index":2,"raw_name":"Naoki Terai","role":"author"}],"license_slug":"ARXIV-1.0","language":"en","version":"v1","ext_ids":{"arxiv":"1107.0563v1"},"release_year":2011,"release_date":"2011-07-04","release_stage":"submitted","release_type":"article","webcaptures":[],"filesets":[],"files":[{"release_ids":["5duhhs3tozbzbkr6f2exomffte"],"mimetype":"application/pdf","urls":[{"url":"https://archive.org/download/arxiv-1107.0563/1107.0563.pdf","rel":"archive"}],"sha256":"4d51b99c85128151fca2a3299dab5a06fa5998fc46f6417379ea86a69d798680","sha1":"a5826dc3c26452e5d87a3572570a543620be93e8","md5":"4debfac8d06d7ea6a3d674736c186f21","size":251692,"revision":"c1efb266-d444-40b8-9229-a3069cc6e2b9","ident":"kymdykk7jrfkdbc5r75hd6cuka","state":"active"}],"work_id":"ceyugnfvpfg57og3df3wyqudkm","title":"Arithmetical rank of squarefree monomial ideals generated by five\n elements or with arithmetic degree four","state":"active","ident":"5duhhs3tozbzbkr6f2exomffte","revision":"245f213b-9369-4c12-9809-4203bfbeedf7","extra":{"arxiv":{"base_id":"1107.0563","categories":["math.AC"],"comments":"22 pages, to appear in Communications in Algebra"}}}