Modules and homological algebra
Homological algebra is a branch of mathematics that studies algebraic structures through their associated chain complexes and homology groups. It has its origins in algebraic topology, but has since been applied to other areas of mathematics such as algebraic geometry and repre- sentation theory....
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| Format: | Final Year Project |
| Language: | English |
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Nanyang Technological University
2023
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| Online Access: | https://hdl.handle.net/10356/166453 |
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| Institution: | Nanyang Technological University |
| Language: | English |
| Summary: | Homological algebra is a branch of mathematics that studies algebraic structures through
their associated chain complexes and homology groups. It has its origins in algebraic topology,
but has since been applied to other areas of mathematics such as algebraic geometry and repre-
sentation theory. This thesis provides a brief introduction into the theory required for the basic
theory of homological algebra, where the Tor and the Ext will be studied. Some characteriza-
tions between projective modules, Tor and Ext were made. The Tor was also balanced, which
allows for Tor group calculations to be made much easier in the future. |
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