ABSTRACT
If A is a complete lattice then a function Δ which assigns to every left R-module M an element Δ(M) of A will be called a quasidimension function on R-mod with values in A if and only if the following conditions are satisfied:
If 0 → M′ M M″ → 0 is an exact sequence in R-mod then Δ(M) = Δ(M′) ∪ Δ(M″).
If M is the directed union of a directed family {Mi | i ∈ Ω} of submodules then Δ(M) = ∪i∈Ω Δ(Mi).
