Grothendieck groups of algebras with nilpotent annihilators
HTML articles powered by AMS MathViewer
- by Maurice Auslander and Idun Reiten PDF
- Proc. Amer. Math. Soc. 103 (1988), 1022-1024 Request permission
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
- Maurice Auslander and Idun Reiten, Grothendieck groups of algebras and orders, J. Pure Appl. Algebra 39 (1986), no. 1-2, 1–51. MR 816889, DOI 10.1016/0022-4049(86)90135-0
- Hyman Bass, Algebraic $K$-theory, W. A. Benjamin, Inc., New York-Amsterdam, 1968. MR 0249491 J. Herzog and H. Sanders, The Grothendieck group of invariant rings and of simple hypersurface singularities,
- Susan Montgomery, Fixed rings of finite automorphism groups of associative rings, Lecture Notes in Mathematics, vol. 818, Springer, Berlin, 1980. MR 590245
Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 103 (1988), 1022-1024
- MSC: Primary 13D15; Secondary 19A49
- DOI: https://doi.org/10.1090/S0002-9939-1988-0954976-9
- MathSciNet review: 954976