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The second part of course in basic algebra is concerned with divisibilty in commmutative domains, extensions of fields and
basic properties of the notion variety.
Last update: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (08.06.2022)
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To pass the practicals and get "Zápočet", one needs to obtain a minimal amount of points in three written homework assignments. Last update: Kompatscher Michael, Ph.D. (19.02.2024)
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The course will follow the lecture notes of David Stanovsky, an English translation will be uploaded throughout the semester on Michael Kompatscher's website https://www.karlin.mff.cuni.cz/~kompatscher/teaching/alg1_cz.pdf.
Other resources:
S. Lang. Algebra, 3rd ed. New York 2002, Springer. S. MacLane, G. Birkhoff. Algebra 3rd ed, Providence 1999, AMS Chelsea publishing company. Stanley N. Burris, H.P. Sankappanavar. A Course in Universal Algebra, The Millenium Edition, Waterloo 2012. URL: https://www.math.uwaterloo.ca/~snburris/htdocs/ualg.html Last update: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (07.02.2025)
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The course is ended by a written test containing 5 questions (students will have 120 minutes of time standardly, which can be extended if a student needs more time). Last update: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (07.02.2025)
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1. Homomorphisms (group homomorphism, quotient groups, ring homomorphisms, ideals, classification of finite fields) 2. Number fields (ring and field extensions, algebraic elements, and finite degree extensions) 3. Algorithms in polynomial arithmetic (fast polynomial multiplication and division, decomposition) 4. Further algebraic structures (lattices and Boolean algebras) Last update: Kompatscher Michael, Ph.D. (07.02.2023)
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The material covered in Algebra 1, and basic knowledge of linear algebra. Last update: Kompatscher Michael, Ph.D. (07.02.2023)
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