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Syzygies and Minimal Resolutions

Johnson, FEA; (2017) Syzygies and Minimal Resolutions. In: Geometry in advanced pure mathematics. (pp. 193-226). World Scientific: Singapour, Singapour. Green open access

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Abstract

The essence of linear algebra over a field resides in the fact that every vector space is free; that is, has a spanning set of linearly independent vectors. The study of linear algebra over more general rings attempts to approximate this situation by the method of free resolutions. When a module M is not free we make a first approximation to its being free by taking a surjective homomorphism ∊ : F0 → M where F0 is free to obtain an exact sequence.

Type: Book chapter
Title: Syzygies and Minimal Resolutions
Open access status: An open access version is available from UCL Discovery
DOI: 10.1142/9781786341082_0006
Publisher version: https://www.worldscientific.com/worldscibooks/10.1...
Language: English
Additional information: Copyright @ 2017 with permission from World Scientific Publishing Co. Pte. Ltd.
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/1527566
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