Illinois Journal of Mathematics

A cancellation theorem for generalized Swan modules

F. E. A. Johnson

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The module cancellation problem asks whether, given modules X, X and Y over a ring Λ, the existence of an isomorphism XYXY implies that XX. When Λ is the integral group ring of a metacyclic group G(p,q), results of Klingler show that the answer to this question is generally negative. By contrast, in this case we show that cancellation holds when Y=Λ and X is a generalized Swan module.

Article information

Illinois J. Math., Volume 63, Number 1 (2019), 103-125.

Received: 6 June 2018
Revised: 18 January 2019
First available in Project Euclid: 29 May 2019

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 16D70: Structure and classification (except as in 16Gxx), direct sum decomposition, cancellation
Secondary: 20C10: Integral representations of finite groups


Johnson, F. E. A. A cancellation theorem for generalized Swan modules. Illinois J. Math. 63 (2019), no. 1, 103--125. doi:10.1215/00192082-7600042.

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