Ideals in the Ring of Colombeau Generalized Numbers
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Publication:3579897
DOI10.1080/00927870903055222zbMath1198.13022arXiv0707.0698OpenAlexW2069108324MaRDI QIDQ3579897
Publication date: 11 August 2010
Published in: Communications in Algebra (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0707.0698
Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.) (46F30) Ordered rings (13J25)
Related Items (16)
Nonlinear generalized sections of vector bundles ⋮ Off-diagonal condition ⋮ New topologies on Colombeau generalized numbers and the Fermat-Reyes theorem ⋮ Differential calculus and integration of generalized functions over membranes ⋮ A Convenient Notion of Compact Set for Generalized Functions ⋮ Algebraic theory of Colombeau's generalized numbers ⋮ Topological and algebraic structures on the ring of Fermat reals ⋮ Strongly internal sets and generalized smooth functions ⋮ Maximal closed ideals of the Colombeau algebra of generalized functions ⋮ Hilbert $\widetilde{\mathbb{C}}$-modules: Structural properties and applications to variational problems ⋮ Asymptotic Ideals (Ideals in the Ring of Colombeau Generalized Constants with Continuous Parametrization) ⋮ Symplectic Modules Over Colombeau-Generalized Numbers ⋮ The ring of Colombeau’s full generalized quaternions ⋮ Supremum, infimum and hyperlimits in the non-Archimedean ring of Colombeau generalized numbers ⋮ A nonlinear theory of generalized functions ⋮ Algebras of generalized functions with smooth parameter dependence
Cites Work
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- Convex and pseudoprime ideals in rings of continuous functions
- Neat rings
- Algebra in a localic topos with applications to ring theory
- A nonlinear theory of generalized functions.
- On a class of valuation fields introduced by A. Robinson
- Ring theory and pointfree topology.
- A discontinuous Colombeau differential calculus
- The torsion theory at a prime ideal of a right Noetherian ring
- z-ideals and prime ideals
- Topological structures in Colombeau algebras: Topological \(\widetilde{\mathbb C}\)-modules and duality theory
- \(\sqrt z\)-ideals and \(\sqrt {z^{^\circ}}\)-ideals in \(C(X)\)
- SOME STRUCTURAL PROPERTIES OF THE TOPOLOGICAL RING OF COLOMBEAU'S GENERALIZED NUMBERS
- Closed graph and open mapping theorems for topological $ \tilde \lc $-modules and applications
- Algebraic and Geometric Theory of the Topological Ring of Colombeau Generalized Functions
- Some remarks on functoriality of Colombeau's construction; topological and microlocal aspects and applications
- Prime z-Ideals of C(X) and Related Rings
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