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.
Syzygy. V.I. Danilov (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Syzygy&oldid=18722