Department of Mathematics
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In the previous lecture, I outlined how we can try to measure certain properties of modules by means of functors defined with the aid of certain kinds of pointed modules. I will discuss (at least) the relevant theorems of Zimmermann [1] related to the Ascending Chain Condition on pp-definable subgroups. (The corresponding theorems for DCC are nearly dual to these.)

[1] Wolfgang Zimmermann, Modules with Chain Conditions for Finite Matrix Subgroups, J. Alg. (190), 68–87 (1997).