Introduces the ideal class group Cl(A,B) of a ring extension A ⊆ B as the kernel of the Picard group map induced by base change, recovering classical class groups and Picard groups as special cases.
Matsumura, Commutative Ring Theory, Cambridge University Press, Cambridge, (1989)
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Ideal class group of an extension of rings and Picard group
Introduces the ideal class group Cl(A,B) of a ring extension A ⊆ B as the kernel of the Picard group map induced by base change, recovering classical class groups and Picard groups as special cases.