Math 254a: the Ideal Class Group, and Unit Theorem
نویسنده
چکیده
We recall that Theorem 1.3 allows us to define the ideal class group of a Dedekind domain, and in particular of a ring of integers, as the group of fractional ideals modulo the subgroup of principal ideals. We will prove that in the case of a ring of integers, the ideal class group is finite. In fact, we will shortly give a stronger statement due to Minkowski. Using similar techniques, we will also study the structure of the group of units in a ring of integers. Before we state our theorems, we introduce some notation:
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