Differential Galois theory extends the classical study of algebraic symmetries into the realm of differential equations. This area investigates the relationship between a differential equation’s ...

Arithmetic dynamics investigates the behaviour of iterated functions—often polynomials or rational maps—over number fields and function fields, while Galois theory provides the framework to analyse ...

Transactions of the American Mathematical Society, Vol. 359, No. 2 (Feb., 2007), pp. 827-857 (31 pages) We discuss some of the basic ideas of Galois theory for commutative S-algebras originally ...

Large fields were introduced by Florian Pop in the 1990's and have played an important role in Galois theory. Examples of large fields are pseudo algebraically closed fields, fields which are complete ...

Let k be a field, F a finite subfield and G a connected solvable algebraic matric group defined over F. Conditions on G and k are given which ensure the existence of a Galois extension of k with group ...