ALGEBRA OF NUMBER SYSTEMS
cod. 14881

Academic year 2009/10
3° year of course - Second semester
Professor
Academic discipline
Algebra (MAT/02)
Field
Formazione algebrico-geometrica
Type of training activity
Characterising
60 hours
of face-to-face activities
6 credits
hub:
course unit
in - - -

Learning objectives

<br />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.

Prerequisites

Course of Algebra.

Course unit content

<br />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.

Full programme

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Bibliography

Van Der Waerden: 'Modern Algebra', Springer.

Teaching methods

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Assessment methods and criteria

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Other information

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