## Illinois Journal of Mathematics

### A cancellation theorem for generalized Swan modules

F. E. A. Johnson

#### Abstract

The module cancellation problem asks whether, given modules $X$, $X^{\prime}$ and $Y$ over a ring $\Lambda$, the existence of an isomorphism $X\oplus Y\cong X^{\prime}\oplus Y$ implies that $X\cong X^{\prime}$. When $\Lambda$ 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 $Y=\Lambda$ and $X$ is a generalized Swan module.

#### Article information

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

Dates
Revised: 18 January 2019
First available in Project Euclid: 29 May 2019

https://projecteuclid.org/euclid.ijm/1559116824

Digital Object Identifier
doi:10.1215/00192082-7600042

Mathematical Reviews number (MathSciNet)
MR3959869

Zentralblatt MATH identifier
07064388

#### Citation

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. https://projecteuclid.org/euclid.ijm/1559116824

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