Order (ring theory)
（重定向自Maximal order）
In mathematics, an order in the sense of ring theory is a subring ![\mathcal{O}](/Images/godic/202501/26/aeb29ed2e1ec2353da1748944aef3c2f4620.png")
of a ring ![A](/Images/godic/202501/26/7fc56270e7a70fa81a5935b72eacbe294620.png")
, such that
The last two conditions condition can be stated in less formal terms: Additively, is a free abelian group generated by a basis for A over ![\mathbb{Q}](/Images/godic/202501/26/d45a4aa156a8ac07ab80e7d9cf5fa79f4620.png")
.
More generally for R an integral domain contained in a field K we define to be an R-order in a K-algebra A if it is a subring of A which is a full R-lattice.