Constrained extensions of differential fields

DOI10.1016/S0001-8708(74)80001-0zbMath0279.12103MaRDI QIDQ1394262

E. R. Kolchin

Publication date: 1974

Published in: Advances in Mathematics (Search for Journal in Brave)

Mathematics Subject Classification ID

Model-theoretic algebra (03C60) Differential algebra (12H05)

Related Items (26)

On the computation of the parameterized differential Galois group for a second-order linear differential equation with differential parameters ⋮ A Class of Differential Fields with Minimal Differential Closures ⋮ Differential and difference algebra ⋮ The classification of the semisimple differential algebraic groups and the linear semisimple differential algebraic Lie algebras ⋮ Picard-Vessiot theory for real fields ⋮ Computing differential Galois groups of second-order linear \(q\)-difference equations ⋮ Existence of \(\partial\)-parameterized Picard-Vessiot extensions over fields with algebraically closed constants ⋮ Computing constraint sets for differential fields ⋮ Computation of the unipotent radical of the differential Galois group for a parameterized second-order linear differential equation ⋮ Constrained extensions of real type ⋮ On differential Galois groups of strongly normal extensions ⋮ New classes of parameterized differential Galois groups ⋮ Computation of the difference-differential Galois group and differential relations among solutions for a second-order linear difference equation ⋮ A Galois-theoretic proof of the differential transcendence of the incomplete gamma function ⋮ Difference Galois theory of linear differential equations ⋮ Differential transcendence criteria for second-order linear difference equations and elliptic hypergeometric functions ⋮ Associative rings ⋮ A Chevalley theorem for difference equations ⋮ A Jordan-Hölder theorem for differential algebraic groups ⋮ Differentially closed fields ⋮ The model theory of differential fields revisited ⋮ On model complete differential fields ⋮ The differential Galois theory of strongly normal extensions ⋮ Functional relations for solutions of \(q\)-difference equations ⋮ On central extensions of simple differential algebraic groups ⋮ Effective bound for the geometric Lang conjecture

Cites Work

• The nonminimality of the differential closure
• Introduction to model theory and to the metamathematics of algebra
• The differential closure of a differential field
• [https://portal.mardi4nfdi.de/wiki/Publication:5181684 The Model Theory of Differential Fields of Characteristic p � 0]
• Pro-Algebraic Groups and the Galois Theory of Differential Fields
• Categoricity in Power
• Uniqueness and characterization of prime models over sets for totally transcendental first-order theories
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Constrained extensions of differential fields