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Department of Mathematics and Applications
"Renato Caccioppoli"


Algebraic Structures

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Algebraic structures

Credits

6

Prerequisites

None

Scientific-disciplinary sector (SSD)

MAT/02

Examination method

Oral exam.

Learning objectives

The course aims to explore in depth the methods and contents of the theory of algebraic structures and its applications, with particular regard to semigroups and lattices.

Syllabus

Semigroups and monoids, free semigroups and monoids, their universal property, submonoids of free monoids, presentations of semigroups and monoids. Lattices, modularity, distributivity, complementation and reducibility in lattice theory, Boolean algebras, applications to group theory.

Expected learning
outcomes

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

  • know and understand the topics covered in semigroup theory and lattice theory,
  • can apply the knowledge acquired to connect abstract structures with the corresponding concrete examples, and can illustrate the results and computational techniques acquired,
  • can communicate ideas and solutions clearly, rigorously and effectively to both specialist and non-specialist audiences,
  • can identify the most appropriate methods to analyse a problem related to the course topics and interpret the results correctly.

Learning outcomes
to be assessed

Command of the subject matter, clarity of exposition, rigour in the use of language, confidence in using the notions acquired.