minorfält

A minorfält, in the context of mathematics, refers to a field that is not algebraically closed. More precisely, it is a field extension of a base field, where the extended field does not contain all the roots of every polynomial with coefficients from the base field. For instance, if we consider the field of rational numbers Q, its algebraic closure is the field of algebraic numbers. A field like the real numbers R is a minorfält of the complex numbers C because, for example, the polynomial x^2 + 1 has no roots in R, even though its coefficients are in R. The concept is important in abstract algebra and field theory, particularly when studying the structure of fields and their extensions. Investigating minorfält extensions helps in understanding properties like separability and the existence of normal or Galois extensions. The study of minorfält is crucial for classifying different types of field extensions and understanding their algebraic relationships.