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Tagged with differential-algebra ac.commutative-algebra
4 questions
2
votes
0
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213
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Open problems in differential algebra and affine algebraic geometry
I am currently doing a PhD in differential algebra and affine algebraic geometry at the University of Buenos Aires. I've been struggling to find a list of interesting and big open problems in these ...
6
votes
1
answer
245
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Reference request for results that involve the transcendence degree
Currently I'm reading "On the Decidability of the Real Exponential Field" by Macintyre and Wilkie and the Proof of Theorem 1.1 (page 462-464) uses two algebraic results that involve the ...
- 123
4
votes
0
answers
356
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Jet Nestruev's proof that the exterior derivative $d$ on a real line is not a Kähler differential $d_{C^\infty(\mathbb{R})/\mathbb{R}}$
The relation between the exterior derivative $d:C^\infty(\mathbb{R})\to\Omega^1\mathbb(\mathbb{R})$ and the Kähler differential $d_{C^\infty(\mathbb{R})/\mathbb{R}}:C^\infty(\mathbb{R})\to\Omega_{C^\...
- 1,615
6
votes
0
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867
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How to extend Ritt's theorem on elementary invertible bijective elementary functions?
The elementary functions according to Liouville and Ritt are the functions of a complex variable built up by applying exponentiation, logarithms and/or algebraic operations finitely often. That means, ...
- 1,053