A note on a paper of R. A. Beaumont and R. J. Wisner on torsion–free groups

Abstract EN

In their 1959 paper, Beaumont and Wisner conjectured that if ℜ is a rank two torsion-free ring without zero-divisors, then ℜ+ decomposes as a direct sum U ⊕ V, where U ≅ V and V is not a nil group.

We construct a counter-example to this conjecture.

To further this aim, we consider the problem of finding a ring ℜ without zero-divisors such that ℜ+ is a torsion-free homogenous indecomposable group with rank equal to two.

2000 Mathematics Subject Classification 20K15