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Lecturer(s)
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Kühr Jan, prof. RNDr. Ph.D.
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Course content
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1. Groups, basic examples of groups. Subgroups, partitions. Normal subgroups, quotient groups. Homomorphisms, congruences, the relationship between homomorphisms, congruences and normal subgroups. The centre of a group, inner authomorphisms. The homomorphism theorem, the isomorphism theorems. Direct products. Cyclic groups. Finite abelian groups. Permutation groups, Cayley's theorem. 2. Rings, division rings and integral domains, basic examples. Subrings, ideals, quotient rings. Homomorphisms, congruences, the relationship between homomorphisms, congruences and ideals. The homomorphism theorem. Prime ideals and maximal ideals. Direct products. The characteristic of a ring.
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Learning activities and teaching methods
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Lecture, Monologic Lecture(Interpretation, Training)
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Learning outcomes
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To understand the rudiments of the theory of groups and rings.
Students are familiar with basic concepts and theorems, including their proofs.
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Prerequisites
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unspecified
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Assessment methods and criteria
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Written exam
Credit: attendance at seminars and/or written test (according to the instructor's discretion).
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Recommended literature
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Birkhoff G., MacLane S. (1974). Algebra. Alfa Bratislava.
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Grillet P. A. (2007). Abstract algebra. Springer New York.
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Halaš R., Chajda I. (1999). Cvičení z algebry. VUP Olomouc.
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Chajda I. (2005). Úvod do algebry. VUP Olomouc.
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Krutský F. (1995). Algebra I. VUP Olomouc.
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Rachůnek J. (2005). Grupy a okruhy. VUP Olomouc.
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Stanovský D. (2010). Základy algebry. Matfyzpress Praha.
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