{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T18:42:09Z","timestamp":1760121729633},"reference-count":7,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2009,5]]},"abstract":"<jats:p> The space of marked commutative rings on n given generators is a compact metrizable space. We compute the Cantor\u2013Bendixson rank of any member of this space. For instance, the Cantor\u2013Bendixson rank of the free commutative ring on n generators is \u03c9<jats:sup>n<\/jats:sup>, where \u03c9 is the smallest infinite ordinal. More generally, we work in the space of finitely generated modules over a given commutative ring. <\/jats:p>","DOI":"10.1142\/s0218196709005068","type":"journal-article","created":{"date-parts":[[2009,5,19]],"date-time":"2009-05-19T10:51:17Z","timestamp":1242730277000},"page":"373-382","source":"Crossref","is-referenced-by-count":4,"title":["THE SPACE OF FINITELY GENERATED RINGS"],"prefix":"10.1142","volume":"19","author":[{"given":"YVES","family":"CORNULIER","sequence":"first","affiliation":[{"name":"IRMAR, Campus de Beaulieu, 35042 Rennes Cedex, France"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/0022-4049(71)90002-8"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1081\/AGB-120022212"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2006.02.012"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1016\/0022-4049(73)90030-3"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1081\/AGB-120004483"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1081\/AGB-120023976"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1016\/0022-4049(73)90039-X"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196709005068","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T13:34:55Z","timestamp":1565184895000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196709005068"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,5]]},"references-count":7,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2009,5]]}},"alternative-id":["10.1142\/S0218196709005068"],"URL":"https:\/\/doi.org\/10.1142\/s0218196709005068","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,5]]}}}