Order (ring theory)

（重定向自Maximal order）

In mathematics, an order in the sense of ring theory is a subring $\mathcal{O}$ of a ring $A$ , such that

The last two conditions condition can be stated in less formal terms: Additively, $\mathcal{O}$ is a free abelian group generated by a basis for A over $\mathbb{Q}$ .

More generally for R an integral domain contained in a field K we define $\mathcal{O}$ to be an R-order in a K-algebra A if it is a subring of A which is a full R-lattice.

单词	Maximal order
释义	Maximal order 英语百科 Order (ring theory) （重定向自Maximal order） In mathematics, an order in the sense of ring theory is a subring $\mathcal{O}$ of a ring $A$ , such that The last two conditions condition can be stated in less formal terms: Additively, $\mathcal{O}$ is a free abelian group generated by a basis for A over $\mathbb{Q}$ . More generally for R an integral domain contained in a field K we define $\mathcal{O}$ to be an R-order in a K-algebra A if it is a subring of A which is a full R-lattice.
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