ABSTRACT
Some of the methods and notions originating in abelian group theory can be dualized, and generalized to the setting of modules over non-perfect rings. We deal with two recent instances of this fact, dualizing and generalizing the notions of a slender group, and an almost free group. In Section 1, we survey the structure theory of dually slender modules and of steady rings (i.e. the rings over which all dually slender modules are finitely generated). In Section 2, strongly uniform modules of infinite dimension, κ, are introduced as duals of κ-free modules. We define their (dual) Γ-invariants. In contrast with the κ-free case, we show that κ ¯ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780367810603/b7b45e7e-db6c-4882-a65d-08c75e14529e/content/inequ25_471_1.tif"/> is the only possible value of the invariants for strongly uniform modules of uncountable dimension κ over a ring R provided that either (i) R is commutative, or (ii) R has a right Krull dimension.
