I'm looking for good references for ideal class groups.
I have studied ideal class groups in two different context; in Algebraic number theory and in Quaternion Algebra (as they have connections with ordinary/supersingular elliptic curves whose endomorphism rings are isomorphic to orders in imaginary quadratic fields or orders in quaterinon algebras over $\mathbb{Q}$).
In both cases, we start from a Dedekind domain $R$. Even in Algebraic number theory, foundational theories are proved and the definition of ideal class group was given in a more general setting; $R$ is a Dedekind domain with field of fractions $K$, and $S$ is the integral closure of $R$ in a finite separable extension $L$ of $K$. However, a few textbooks for Algebraic number theory I have studied all take $R$ to be the ring of integers of a number field when they actually prove some properties of the ideal class group (e.g. finiteness of class numbers).
Ideal class groups of orders in Quaternion algebras are quite analogous to the previous, but again in his book "Quaternion algebras", Voight states the results for Quaternion algebras over $\mathbb{Q}$ or over number fields in general. There is some added complexity like non-commutativity, but it still sounds quite specific. He often built theories on the case where $R$ is a Dedekind domain with field of fractions $K$ and $B$ is a (central simple) $K$-algebra and I'm wondering if there are some generalizations over $K$-algebras?
If you can introduce me some good graduate textbooks or lecture notes, that would be much appreciated.
Added: I just found a post about this topic on Overflow:
Is there a "purely algebraic" proof of the finiteness of the class number?
Stasinski wrote a paper, proving the following theorem stating a sufficient condition for a Dedekind domain to have a finite class number.
[Theorem] Let $A$ be a basic PID and let $B$ be a Dedekind domain which is finitely generated and free as an $A$-module. Then $B$ has finite ideal class group.