Abstract
Abstract Suppose that R is a finite-dimensional algebra. There are algebraic and model- theoretic measures of the complexity of the category of R-modules. On the surface there is no reason to expect a strong correlation between these measures. Nevertheless for the (types of) algebras examined there is such a connection. The algebraic and model-theoretic background is described and the evidence for a correlation in general is presented. This has bearing on the question of which rings have decidable theory of modules. I begin by setting the scene.
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