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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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The course introduces general algebraic constructions and main results of universal algebra. The introduction is devoted to algebras and basic algebraic constructions: subalgebras, morphisms, products, subdirect representations, etc. Further parts of the course introduce classes of algebras definable by identities and quasiidentities and their characterization as classes of algebras closed under certain class operators (Birkhoff's variety theorem, characterization of quasivarieties). The final part of the course is aimed as selected topics from universal algebra: selected properties of varieties, primality, and functional completeness. 1. Algebras, subalgebras, and morphisms
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Learning activities and teaching methods
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Lecture
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Learning outcomes
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To introduce the general algebraic constructions and main results of universal algebra to students.
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, New York.
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Denecke K., Wismath S. L. (2001). Universal Algebra and Applications in Computer. Chapman & Hall/CRC.
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Gratzer G. (1979). Universal Algebra. Springer-Verlag Berlin Heidelberg (druhé vydání).
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Chajda I., Glazek K. (2002). A Basic Course on General Algebra. Technical University Press, Zielona Góra.
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Ježek J. (1976). Univerzální algebra a teorie modelů. SNTL Praha.
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Michael J. O'Donnell. (1985). Equational Logic as a Programming Language. MIT Press.
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Wechler W. (1992). Universal Algebra for Computer Scientists. Springer-Verlag Berlin Heidelberg.
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