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2008 Noncoherence of a Causal Wiener Algebra Used in Control Theory
Amol Sasane
Abstr. Appl. Anal. 2008: 1-13 (2008). DOI: 10.1155/2008/459310

Abstract

Let 0 : = { s Re ( s ) 0 } , and let 𝒲 + denote the ring of all functions f : 0 such that f ( s ) = f a ( s ) + k = 0 f k e s t k ( s 0 ) , where f a L 1 ( 0 , ) , ( f k ) k 0 1 , and 0 = t 0 < t 1 < t 2 < equipped with pointwise operations. (Here ^ denotes the Laplace transform.) It is shown that the ring 𝒲 + is not coherent, answering a question of Alban Quadrat. In fact, we present two principal ideals in the domain 𝒲 + whose intersection is not finitely generated.

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Amol Sasane. "Noncoherence of a Causal Wiener Algebra Used in Control Theory." Abstr. Appl. Anal. 2008 1 - 13, 2008. https://doi.org/10.1155/2008/459310

Information

Published: 2008
First available in Project Euclid: 9 September 2008

zbMATH: 1159.46032
MathSciNet: MR2429624
Digital Object Identifier: 10.1155/2008/459310

Rights: Copyright © 2008 Hindawi

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