Course title:Abstract Arithmetic
Faculty:Faculty of Education
Department:Department of Mathematics with Didactics
Course code:KMD / E-AG3
Semester:Winter / Summer
Level of study:Mgr.
Format of study:Lecture 1 [Hours/Week], Seminar 1 [Hours/Week]
Name of the lecturer:Ing. Tomáš Barot, Ph.D. (G)
Language:English, German
ISCED F broad:Natural sciences, mathematics and statistics
Annotation:The course introduces methods of construction of number fields - construction of natural numbers using Pean's axioms, natural numbers in the sense of an algebraic structure, a splitting group and a splitting field, construction of the ring of integers and rational numbers, embedding of a lattice into a complete lattice, MacNeil's hull, construction of real numbers in the sense of completion rational numbers, two method of construction - Dedeknid's cuts, topological completion using Cauchy sequences, an algebraic complete field, construction of the field of complex numbers, an algebraic complete field of complex numbers, divisibility in integral domains, special types of integral domains with special arithmetic properties, Gauss rings, a principal ideal ring, Euclidean rings.