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Università degli Studi di Parma Università degli Studi di Parma
University of Parma
Course catalogue
Università degli Studi di Parma
course catalogue

ALGEBRA OF NUMBER SYSTEMS
cod. 14881

borrowed from Corso di TIPO in CDS 0275 - ALGEBRA DEI SISTEMI NUMERICI - cod. 14881
Academic year 2008/09
3° year of course - Second semester
Professor
Giordano GALLINA
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 - - -
lectures timetable unavailable
exam calls
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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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2030 agenda goals for sustainable development

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