Abstract

Let [Formula: see text] be an order in a quadratic number field [Formula: see text] with ring of integers [Formula: see text], such that the conductor [Formula: see text] is a prime ideal of [Formula: see text], where [Formula: see text] is a prime. We give a complete description of the [Formula: see text]-primary ideals of [Formula: see text]. They form a lattice with a particular structure by layers; the first layer, which is the core of the lattice, consists of those [Formula: see text]-primary ideals not contained in [Formula: see text]. We get three different cases, according to whether the prime number [Formula: see text] is split, inert or ramified in [Formula: see text].

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