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Department of Mathematics and Applications
"Renato Caccioppoli"


Algebra 2

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Algebra 2

Credits

6

Prerequisites

Algebra 1

Scientific-disciplinary sector (SSD)

MAT/02 Algebra

Examination method

Oral exam.

Learning
objectives

The course aims to develop further critical knowledge of the contents and methods of modern Algebra, continuing the study of algebraic structures begun in the Algebra 1 course, with particular attention to ring and field structures.

Syllabus

General properties of rings; factorial, principal and Euclidean rings; polynomial rings, with particular reference to those with coefficients in a field; fields, degrees of extensions, algebraic extensions, splitting fields, algebraically closed fields; finite fields: order, additive and multiplicative structure, uniqueness up to isomorphism for fields of a given order; the automorphism group of a field.

Expected learning
outcomes

At the end of the course, students must demonstrate that they:

  • know and understand the topics covered in ring theory and field theory;
  • are able to apply the knowledge acquired to link abstract settings smoothly with the corresponding concrete examples, as well as to formulate and understand statements;
  • are able to communicate ideas and solutions clearly, rigorously and effectively to both specialist and non-specialist audiences;
  • are able to identify the most appropriate methods to analyse and solve a problem related to the course topics and to interpret the results correctly.

Learning outcomes
to be assessed

Command of the knowledge acquired, clarity of presentation, rigour in the use of language, confidence in using the notions acquired.