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.
Lam, A First Course in Noncommutative Rings, Spring er-Verlag, (2001)
2 Pith papers cite this work. Polarity classification is still indexing.
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Localization of an M-graded ring at homogeneous elements yields a G-graded ring with G the Grothendieck group of M.
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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.
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Grading of homogeneous localization by the Grothendieck group
Localization of an M-graded ring at homogeneous elements yields a G-graded ring with G the Grothendieck group of M.