Order (ring theory): Difference between revisions
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In [[ring theory]], an '''order''' is a [[ring (mathematics)|ring]] which is finitely generated as a '''Z'''-module. | In [[ring theory]], an '''order''' is a [[ring (mathematics)|ring]] which is finitely generated as a '''Z'''-module. | ||
Any [[subring]] of an [[algebraic number field]] composed of [[algebraic integer]]s forms an order: the ring of all algebraic integers in such a field is the ''maximal order''. | Any [[subring]] of an [[algebraic number field]] composed of [[algebraic integer]]s forms an order: the ring of all algebraic integers in such a field is the ''maximal order''. | ||
Revision as of 12:58, 1 February 2009
In ring theory, an order is a ring which is finitely generated as a Z-module.
Any subring of an algebraic number field composed of algebraic integers forms an order: the ring of all algebraic integers in such a field is the maximal order.