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- Syzygy_(mathematics) abstract "In mathematics, a syzygy (from Greek συζυγία 'pair') is a relation between the generators of a module M. The set of all such relations is called the \"first syzygy module of M\". A relation between generators of the first syzygy module is called a \"second syzygy\" of M, and the set of all such relations is called the \"second syzygy module of M\". Continuing in this way, we derive the nth syzygy module of M by taking the set of all relations between generators of the (n − 1)th syzygy module of M. If M is finitely generated over a polynomial ring over a field, this process terminates after a finite number of steps; i.e., eventually there will be no more syzygies (see Hilbert's syzygy theorem). The syzygy modules of M are not unique, for they depend on the choice of generators at each step.The sequence of the successive syzygy modules of a module M is the sequence of the successive images (or kernels) in a free resolution of this module.Buchberger's algorithm for computing Gröbner bases allows the computation of the first syzygy module: The reduction to zero of the S-polynomial of a pair of polynomials in a Gröbner basis provides a syzygy, and these syzygies generate the first module of syzygies.".
- Syzygy_(mathematics) wikiPageExternalLink what-is.pdf.
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- Syzygy_(mathematics) wikiPageRevisionID "688295507".
- Syzygy_(mathematics) wikiPageWikiLink Buchbergers_algorithm.
- Syzygy_(mathematics) wikiPageWikiLink Category:Module_theory.
- Syzygy_(mathematics) wikiPageWikiLink Field_(mathematics).
- Syzygy_(mathematics) wikiPageWikiLink Generator_(mathematics).
- Syzygy_(mathematics) wikiPageWikiLink Greek_language.
- Syzygy_(mathematics) wikiPageWikiLink Gröbner_basis.
- Syzygy_(mathematics) wikiPageWikiLink Hilberts_syzygy_theorem.
- Syzygy_(mathematics) wikiPageWikiLink Mathematics.
- Syzygy_(mathematics) wikiPageWikiLink Module_(mathematics).
- Syzygy_(mathematics) wikiPageWikiLink Polynomial_ring.
- Syzygy_(mathematics) wikiPageWikiLink Resolution_(algebra).
- Syzygy_(mathematics) wikiPageWikiLinkText "Syzygy (mathematics)".
- Syzygy_(mathematics) wikiPageWikiLinkText "Syzygy".
- Syzygy_(mathematics) wikiPageWikiLinkText "syzygies".
- Syzygy_(mathematics) wikiPageWikiLinkText "syzygy".
- Syzygy_(mathematics) id "p/s091990".
- Syzygy_(mathematics) title "Syzygy".
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- Syzygy_(mathematics) wikiPageUsesTemplate Template:Citation.
- Syzygy_(mathematics) wikiPageUsesTemplate Template:Other_uses.
- Syzygy_(mathematics) wikiPageUsesTemplate Template:Springer.
- Syzygy_(mathematics) subject Category:Module_theory.
- Syzygy_(mathematics) hypernym Relation.
- Syzygy_(mathematics) type Agent.
- Syzygy_(mathematics) comment "In mathematics, a syzygy (from Greek συζυγία 'pair') is a relation between the generators of a module M. The set of all such relations is called the \"first syzygy module of M\". A relation between generators of the first syzygy module is called a \"second syzygy\" of M, and the set of all such relations is called the \"second syzygy module of M\". Continuing in this way, we derive the nth syzygy module of M by taking the set of all relations between generators of the (n − 1)th syzygy module of M.".
- Syzygy_(mathematics) label "Syzygy (mathematics)".
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- Syzygy_(mathematics) sameAs Q2377256.
- Syzygy_(mathematics) wasDerivedFrom Syzygy_(mathematics)?oldid=688295507.
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