ALGEBRA OF NUMBER SYSTEMS
Learning outcomes of the course unit
To introduce generalizations of the notion of the ordering of the field of real numbers and of the notion on absolute value of the real field.
Course of Algebra.
Course contents summary
Near-ordered and partially ordered monoids and groups. Ordered fields. Ordered extensions. Theorem of Artin-Schreier. Algebrically closed fields, algebraic closures. Maximal ordered fields. Symmetric polynomials. Theorem of Euler-Lagrange. Absolute values onto fields. Archimedean and non Archimedean absolute values. Equivalence. Charecterization of the absolute values on the rational field and onto K(X). Completions.
Van Der Waerden: 'Modern Algebra', Springer.