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1. Galois theory: In mathematics, Galois theory, originally introduced by Évariste Galois, provides a connection between field theory and group theory. This connection, the fundamental theorem of Galois theory, allows reducing certain problems in field theory to group theory, which makes them simpler ... (Mathematical connection between field theory and group theory) [100%] 2023-12-07 [Galois theory]
2. Galois theory: Galois theory is an area of mathematical study that originated with Evariste Galois around 1830, as part of an effort to understand the relationships between the roots of polynomials, in particular why there are no simple formulas for extracting the ... [100%] 2023-07-20
3. Galois theory: In the most general sense, Galois theory is a theory dealing with mathematical objects on the basis of their automorphism groups. For instance, Galois theories of fields, rings, topological spaces, etc., are possible. (Mathematics) [100%] 2023-10-12
4. Galois theory: In mathematics, Galois theory, originally introduced by Évariste Galois, provides a connection between field theory and group theory. This connection, the fundamental theorem of Galois theory, allows reducing certain problems in field theory to group theory, which makes them simpler ... (Mathematical connection between field theory and group theory) [100%] 2025-06-08 [Galois theory]
5. Differential Galois theory: In mathematics, differential Galois theory studies the Galois groups of differential equations. Whereas algebraic Galois theory studies extensions of algebraic fields, differential Galois theory studies extensions of differential fields, i.e. (Study of Galois symmetry groups of differential fields) [81%] 2023-10-09 [Field theory] [Differential algebra]...
6. Topological Galois theory: In mathematics, topological Galois theory is a mathematical theory which originated from a topological proof of Abel's impossibility theorem found by V. I. [81%] 2023-09-12 [Galois theory] [Topology]...
7. Differential Galois theory: In mathematics, differential Galois theory is the field that studies extensions of differential fields. Whereas algebraic Galois theory studies extensions of algebraic fields, differential Galois theory studies extensions of differential fields, i.e. (Study of Galois symmetry groups of differential fields) [81%] 2025-06-08 [Galois theory] [Differential algebra]...
8. Galois theory of rings: A generalization of the results of the theory of Galois fields (cf. Galois theory and Galois group) to the case of associative rings with a unit element. (Mathematics) [70%] 2023-10-30
9. Grothendieck s Galois theory: In mathematics, Grothendieck's Galois theory is an abstract approach to the Galois theory of fields, developed around 1960 to provide a way to study the fundamental group of algebraic topology in the setting of algebraic geometry. It provides, in ... [70%] 2024-08-05 [Galois theory] [Algebraic geometry]...
10. Fundamental theorem of Galois theory: In mathematics, the fundamental theorem of Galois theory is a result that describes the structure of certain types of field extensions. In its most basic form, the theorem asserts that given a field extension E/F that is finite and ... [63%] 2023-11-03 [Field theory] [Theorems in group theory]...
11. Fundamental theorem of Galois theory: In mathematics, the fundamental theorem of Galois theory is a result that describes the structure of certain types of field extensions in relation to groups. It was proved by Évariste Galois in his development of Galois theory. (Correspondence between subfields and subgroups) [63%] 2025-05-25 [Theorems in group theory] [Galois theory]...
12. Resolvent (Galois theory): In Galois theory, a discipline within the field of abstract algebra, a resolvent for a permutation group G is a polynomial whose coefficients depend polynomially on the coefficients of a given polynomial p and has, roughly speaking, a rational root ... (Galois theory) [81%] 2024-04-13 [Group theory] [Galois theory]...
13. Galois theory#Related Articles: A list of Citizendium articles, and planned articles, about Galois theory. See also changes related to Galois theory, or pages that link to Galois theory or to this page or whose text contains "Galois theory". Contents * 1 Parent topics * 2 ... [70%] 2025-04-26
14. Galois theory, inverse problem of: The problem of constructing a finite normal extension of a given field $k$ with given Galois group (cf. Galois theory), and of stating the conditions which ensure the existence (and non-existence) of such an extension over $k$. (Mathematics) [63%] 2023-10-23 [Field theory and polynomials]