Topic Archive: Modules
We will review the definitions of morphic rings and modules, and prove a result concerning conditions equivalent to total uniform morphicity of a ring (all R-modules being morphic in a uniform way). We consider questions such as, which abelian groups are morphic, and when products of morphic modules are morphic. This will lead us to a discussion of the Ziegler spectrum, and its relation to morphicness.
I will review the notions of VC-dimension, VC-density, and breadth on modules, before describing and motivating some partial results to open questions from a paper by Aschenbrenner, Dolich, Haskell, Macpherson, and Starchenko.