ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

2. Algebra

1991 MS Classification: 16 Meyer, Johan, University of the Orange Free State, South Africa Forcing Linearity Numbers Let R be a ring with identity and V a unital R-module and consider the set M_{R}(V) = {f : V → V |f(rv) = rf(v), ∀r ∈ R, ∀v ∈ V }. Under the operations of function addition and composition of maps, M_{R}(V) is a nearring which contains End_{R}(V), the ring of R-endomorphisms of V. A collection S = {W_{α}}_{α∈A} of proper submodules of V is said to force linearity on V if whenever f ∈ Hom_{R}(W_{α}, V) for each α ∈ A, then f ∈ End_{R}(V). The minimum number of proper submodules of V needed to force linearity is called the forcing linearity number for V, denoted by fln(V). We determine the fln for vector spaces, modules over integral domains, not fields, and modules over local rings, not integral domains.