KAG/ALG2D Algebra 1

Lecturers: Radomír Halaš, Petr Emanovský
Lecture: 2 hours/week + tutorial 2 hours/week
Credits: 6
Winter semester
Form of course completion: course credit, exam

• Binary relations, reflexive, symmetric and transitive relations. Equivalence relations and partitions, quotient sets.
• Grupoids, semigroups and groups. Natural and integer powers in semigroups and groups. Homomorphisms and congruence relations, quotient grupoids, the homomorphism theorem for grupoids. Subgroups and normal subgroups of groups. Congruence relations and homomorphisms of groups. Quotient groups. The homomorphism theorem for groups, isomorphism theorems. Subgroup generated by a set, order of a subgroup and of an element. Cyclic groups. Permutation groups, the Cayley theorem.
• Rings, integral domains and fields. Ideals, prime ideals and maximal ideals. Homomorphism and congruence relations, quotient rings. The homomorphism theorem. Order of an element, characteristic of a ring.  Direct products of rings.