Primary decomposition of ideals in a ring
The concept of unique factorization was first recognized in the 1840s, but even then, it was still fairly believed to be automatic. The error of this assumption was exposed largely through attempts to prove Pierre de Fermat's, 1601-1665, last theorem. Once mathematicians discovered that this pr...
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| Format: | Others |
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CSUSB ScholarWorks
2007
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| Online Access: | https://scholarworks.lib.csusb.edu/etd-project/3289 https://scholarworks.lib.csusb.edu/cgi/viewcontent.cgi?article=4373&context=etd-project |
| Summary: | The concept of unique factorization was first recognized in the 1840s, but even then, it was still fairly believed to be automatic. The error of this assumption was exposed largely through attempts to prove Pierre de Fermat's, 1601-1665, last theorem. Once mathematicians discovered that this property did not always hold, it was only natural for them to try to search for the strongest available alternative. Thus began the attempt to generalize unique factorization. Using the ascending chain condition on principle ideals, we will show the conditions under which a ring is a unique factorization domain. |
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