Asymptotic Ideals (Ideals in the Ring of Colombeau Generalized Constants with Continuous Parametrization)

Khélif, Anatole; Scarpalézos, Dimitris; Vernaeve, Hans

doi:10.1080/00927872.2013.772189

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Z G −Sets Z G −Filters1

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2020

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“…Which results of this paper are still valid under this condition? For the case of generalized constants, a first investigation has been done in [18].…”

Section: Z G −Sets Z G −Filtersmentioning

confidence: 99%

Maximal closed ideals of the Colombeau Algebra of Generalized functions

Khélif

Scarpalézos

2020

Monatsh Math

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In this paper we investigate the structure of the set of maximal ideals of $${{\mathcal {G}}}(\Omega )$$ G ( Ω ) . The method of investigation passes through the use of the $$m-$$ m - reduction and the ideas are analoguous to those in Gillman and Jerison (Rings of Continuous Functions, N.J. Van Nostrand, Princeton, 1960) for the investigation of maximal ideals of continuous functions on a Hausdorff space K.

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“…Which results of this paper are still valid under this condition? For the case of generalized constants, a first investigation has been done in [18].…”

Section: Z G −Sets Z G −Filtersmentioning

confidence: 99%