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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Grothendieck groups of algebras with nilpotent annihilators

Authors: Maurice Auslander and Idun Reiten
Journal: Proc. Amer. Math. Soc. 103 (1988), 1022-1024
MSC: Primary 13D15; Secondary 19A49
MathSciNet review: 954976
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Abstract: Let $ R$ be a commutative noetherian ring and $ i:R \to \Lambda $ an $ R$-algebra such that $ \Lambda $ is a finitely generated $ R$-module. Then the annihilator of $ \Lambda $ in $ R$ is nilpotent if and only if the cokernel of the induced map of Grothendieck groups $ {i^*}:{K_0}(\bmod \Lambda )$ is a torsion group.

References [Enhancements On Off] (What's this?)

  • [1] M. Auslander and I. Reiten, Grothendieck groups of algebras and orders, J. Pure Appl. Algebra 29 (1986), 1-51. MR 816889 (87g:16038)
  • [2] H. Bass, Algebraic $ K$-theory, Benjamin, New York, 1968. MR 0249491 (40:2736)
  • [3] J. Herzog and H. Sanders, The Grothendieck group of invariant rings and of simple hypersurface singularities,
  • [4] S. Montgomery, Fixed rings of finite automorphism groups of associative rings, Lecture Notes in Math., vol. 818, Springer-Verlag, Berlin and New York, 1980. MR 590245 (81j:16041)

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