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Transactions of the American Mathematical Society

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$ G\sb{0}$ of a graded ring

Author: Leslie G. Roberts
Journal: Trans. Amer. Math. Soc. 166 (1972), 187-195
MSC: Primary 13J05
MathSciNet review: 0294326
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Abstract: We consider the Grothendieck group $ {G_0}$ of various graded rings, including $ {G_0}(A_n^r)$ where A is a commutative noetherian ring, and $ A_n^r$ is the A-subalgebra of the polynomial ring $ A[{X_0}, \ldots ,{X_n}]$ generated by monomials of degree r. If A is regular, then $ {G_0}(A_n^r)$ has a ring structure. The ideal class groups of these rings are also considered.

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Keywords: Grothendieck group, $ {G_0}$, graded ring, ideal class group
Article copyright: © Copyright 1972 American Mathematical Society

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