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Lecturer(s)
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Chajda Ivan, prof. RNDr. DrSc.
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Course content
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1. Concept of algebras, subalgebras, homomorphisms. Concept of congruence and quotient algebras. 2. Construction of direct and subdirect products. 3. Homomorphism and isomorphism theorems. 4. Operators H, S, P, varieties of algebras. 5. Free algebras, the algebra of terms, identities. 6. Subdirectly irreducible algebras. 7. Deductive closure and equational logics. 8. Congruence conditions. 9. Maltsev conditions on varieties. 10. Congruence distributivity, modularity and permutability, regular varieties. 11. Primal and functionally complete algebras.
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Learning activities and teaching methods
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Lecture
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Learning outcomes
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There are studied basis of universal algebra containing the basic constructions (subalgebra, quotient algebra, direct product), then are studied varieties of algebras (free algebras, subdirectly irreducible algebras). We go on with congruence conditions and the equational logic.
1. Knowledge Advanced theory of universal algebras is presented. Varieties of algebras are treated. Congruence conditions are classified by mens of free algebras.
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Prerequisites
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unspecified
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Assessment methods and criteria
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Oral exam, Written exam
Knowledge of the basic construction (subalgebras, homomorphic images, quotient algebras, direct and subdirect products). Homomorphism and isomorphism theorems. Subdirectly irreducible algebras. Free algebras, terms, induction over the term complexity. Varieties of algebras. Birkhoff theorems. Equacional logic. Congruence conditions.
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Recommended literature
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Burris S., Sankappanavar H.P. (1981). A Course in Universal Algebra. Springer-Verlag, N.Y. (new alectronic vesion, 1999 in Internet).
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Grätzer G. (1979). Universal Algebra, 2nd ed.. Springer-Verlag, New York.
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Chajda I., Glazek K. (2000). A Basic Course on General Algebra. Technical University Press, Zielona Góra.
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