Some algebraic properties of the Wiener-Laplace algebra

• Autorzy: Mortini R. , Sasane A.
• Języki publikacji: PL

Abstrakty

EN

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.

Słowa kluczowe

PL

algebra Wienera-Laplace'a; teoria sterowania

EN

GCD domain; Wiener-Laplace algebra; control theory

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2010
• Tom: Vol. 16, nr 1
• Strony: 79--94
• Opis fizyczny: Bibliogr. 24 poz.

Twórcy

autor

Mortini R.

autor

Sasane A.

• Département de Mathématiques et LMAM, Université Paul Verlaine, Ile du Saulcy, 57045 Metz, France,

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