Order (ring theory)

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

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

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