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An astronomical term denoting the disposition of three celestial bodies on a line.

In algebra it is used in the sense of a relationship. Let be a left -module, and let be a family of elements of ; a relationship, or syzygy, between the is a set of elements of the ring such that . Thus there arises the module of syzygies, the chain complex of syzygies, etc. See Hilbert theorem on syzygies.


Syzygies appear in the definition of syzygetic ideals and the theory of regular algebras and regular sequences, cf. Koszul complex; Depth of a module.

How to Cite This Entry:
Syzygy. V.I. Danilov (originator), Encyclopedia of Mathematics. URL:
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098