Abstract
We denote by W+(ℂ+) the set of all complex-valued functions defined in the closed right half plane ℂ+ ≔ {s ∈ ℂ | Re(s) ≥ 0} that differ from the Laplace transform of functions from L1(0, ∞) by a constant. Equipped with pointwise operations, W+(ℂ+) forms a ring. It is known that W+(ℂ+) is a pre-Bézout ring. The following properties are shown for W+(ℂ+):
W+(ℂ+) is not a GCD domain, that is, there exist functions F1, F2 in W+(ℂ+) that do not possess a greatest common divisor in W+(ℂ+).
W+(ℂ+) is not coherent, and in fact, we give an example of two principal ideals whose intersection is not finitely generated.
We will also observe that W+(ℂ+) is a Hermite ring, by showing that the maximal ideal space of W+(ℂ+), equipped with the Gelfand topology, is contractible.
© de Gruyter 2010
