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.
Bass, Algebraic K-Theory, W.A
2 Pith papers cite this work. Polarity classification is still indexing.
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Proves exact sequence 0 → Pic(A) → K0(A)* → B(A) → 0 for any commutative ring A, with B(A) ≅ B(K0(A)) ≅ H0(A)*, split exactness for Dedekind domains, and applications to idempotent lifting and projective module supports.
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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.
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On the Grothendieck ring and the relation of its group of units with the Picard group
Proves exact sequence 0 → Pic(A) → K0(A)* → B(A) → 0 for any commutative ring A, with B(A) ≅ B(K0(A)) ≅ H0(A)*, split exactness for Dedekind domains, and applications to idempotent lifting and projective module supports.