Name of some specific orders in number fields Let $\mathbb{K}/\mathbb{Q}$ a number field. For an integer $\theta\in\mathfrak{o}_\mathbb{K}$, one can define an order $$ \mathbb{Z}[\theta] = \oplus_i \mathbb{Z} \theta^i. $$ Is there a canonical naming for this kind of orders? _Monogeneous orders? Principal orders_ , like for ideals?

The computer algebra system `magma` calls such a thing an _equation order_.

It is isomorphic to the ring $\mathbb{Z}[x]/(f(x))$, where $f$ is the minimal polynomial for $\theta$ over $\mathbb{Q}$.

The specific basis $\\{ \theta^i \\}$ would be called a _power basis_.