Abstract
We prove that every serial ring R has the isolation property: every isolated point in any theory of modules over R is isolated by a minimal pair. Using this we calculate the Krull–Gabriel dimension of the module category over serial rings. For instance, we show that this dimension cannot be equal to 1.
Acknowledgment
This paper was written during the visit of the author to the University of Manchester supported by EPSRC grant GR/R44942/01. He would like to thank the University for the kind hospitality.