[{"key":"dc.contributor.author","value":"Carson, Andrew Bruce","language":null},{"key":"dc.date.accessioned","value":"2011-03-30T20:36:34Z","language":null},{"key":"dc.date.available","value":"2011-03-30T20:36:34Z","language":null},{"key":"dc.date.issued","value":"1971","language":null},{"key":"dc.identifier.uri","value":"http:\/\/hdl.handle.net\/2429\/33106","language":null},{"key":"dc.description.abstract","value":"A commutative ring is called coherent if the intersection of any two finitely generated ideals is finitely generated and the annihilator ideal of an arbitrary element of the ring is finitely generated.\r\nPierce's representation of a ring R as the ring of all global sections of an appropriate sheaf of rings, k , is described. Some theorems are deduced relating the coherence of the ring R to certain properties of the sheaf k . The sheaves from the above representation\r\nfor R\u2308X\u2309 and R\u2308\u2308G\u207a\u2309\u2309 , where R is a commutative von Neumann regular ring and G is a linearly ordered abelian group, are calculated. Applications of the above theorems now show that R\u2308X\u2309 is coherent and yield necessary and sufficient conditions for R\u2308\u2308G\u207a\u2309\u2309  to be coherent.","language":"en"},{"key":"dc.language.iso","value":"eng","language":"en"},{"key":"dc.publisher","value":"University of British Columbia","language":"en"},{"key":"dc.rights","value":"For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https:\/\/open.library.ubc.ca\/terms_of_use.","language":null},{"key":"dc.title","value":"Sheaf methods applied to coherent rings","language":"en"},{"key":"dc.type","value":"Text","language":"en"},{"key":"dc.degree.name","value":"Doctor of Philosophy - PhD","language":"en"},{"key":"dc.degree.discipline","value":"Mathematics","language":"en"},{"key":"dc.degree.grantor","value":"University of British Columbia","language":"en"},{"key":"dc.type.text","value":"Thesis\/Dissertation","language":"en"},{"key":"dc.description.affiliation","value":"Science, Faculty of","language":null},{"key":"dc.description.affiliation","value":"Mathematics, Department of","language":null},{"key":"dc.degree.campus","value":"UBCV","language":"en"},{"key":"dc.description.scholarlevel","value":"Graduate","language":"en"}]