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Weak ideal invariance and orders in artinian rings: Corrigendum

Published online by Cambridge University Press:  17 April 2009

John A. Beachy
John A. Beachy
Affiliation:
Department of Mathematical Sciences, Northern Illinois University, DeKalb, Illinois 60115, USA.
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Let R be an associative ring with identity element which has Krull dimension on the left (see [3] for the relevant definitions). For any ordinal α, and any module RX, let τα(X) denote the sum in. X of all cyclic submodules of Krull dimension less than α. (The Krull dimension of a module X will be denoted by |x|.) It is clear that if X' is a submodule of X, then τα(X) = X' ∩ τα(X) and that f[τα(X)] ⊆ τα(Y) for any R-homomorphism f: X→Y. Thus τα defines a torsion preradical.

Type
Corrigendum
Information
Bulletin of the Australian Mathematical Society , Volume 25 , Issue 2 , April 1982 , pp. 317 - 320
Copyright
Copyright © Australian Mathematical Society 1982

References

[1]Beachy, John A., “Weak ideal invariance and orders in Artinian rings”, Bull. Austral. Math. Soc. 23 (1981), 255–264.CrossRefGoogle Scholar
[2]Brown, K.A., Lenagan, T.H. and Stafford, J.T., “Weak ideal invariance and localisation”, J. London Math. Soc. (2) 21 (1980), 53–61.CrossRefGoogle Scholar
[3]Gordon, Robert and Robson, J.C., Krull dimension (Memoirs of the American Mathematical Society, 133. American Mathematical Society, Providence, Rhode Island, 1973).Google Scholar
[4]Krause, Gunter, Lenagan, T.H. and Stafford, J.T., “Ideal invariance and Artinian quotient rings”, J. Algebra 55 (1978), 145–154.CrossRefGoogle Scholar