Journal
COMMUNICATIONS IN ALGEBRA
Volume 38, Issue 6, Pages 2199-2228Publisher
TAYLOR & FRANCIS INC
DOI: 10.1080/00927870903055222
Keywords
Algebras of generalized functions
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Funding
- FWF (Austria) [M949-N18, Y237-N13]
- Austrian Science Fund (FWF) [Y 237] Funding Source: researchfish
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The structure of the ideals in the ring of Colombeau generalized numbers is investigated. Connections with the theories of exchange rings, Gelfand rings and lattice-ordered rings are given. Characterizations for prime, projective, pure, and topologically closed ideals are given, answering in particular the questions about prime ideals in [1]. Also z-ideals [23] are characterized. It is shown that the quotient rings modulo maximal ideals are canonically isomorphic with nonstandard fields of asymptotic numbers and that the Hahn-Banach extension property does not hold for a large class of topological modules over the ring of Colombeau generalized numbers.
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