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1 Journal of Applied Analysis

1 2010

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Some algebraic properties of the Wiener-Laplace algebra

Mortini R., Sasane A.

Journal of Applied Analysis

2010

Vol. 16, nr 1

79-94

We denote by W+(C+) the set of all complex-valued functions defined in the losed right half plane C+ := {s ∈ C | Re(s) ≥ 0} that differ from the Laplace transform of functions from L1 (O, ∞) 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.