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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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Ring and modules Rings, ideals and congruences, quotient rings. Divisibility in integrity domains. Integrity domains of principal ideals. Embedding of an integrity domain into a field. Boolean rings. Embedding of semiring into a ring. Modules, quotient modules. Groups of homomorphismus of modules. Direct products and sums. Free, projective and injective
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Learning activities and teaching methods
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Lecture
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Learning outcomes
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The goal is to get a basic information on the theory of rings and fields.
1. Knowledge Describe advanced basics of algebra, concretely Rings. Integrity domains, fields. Ideals, faktoriaztion. Prime ideals, maximal ideals. Embedding of integrity domains in fields. Modules, groups of homomorphismus of modules, direct products and sums.Free, projective and injective modules. Radicals.
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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
In accordance with the textbook "Rings and modules".
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Recommended literature
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Herman J.,Kučera R., Šimša J. (1997). Metody řešení matematických úloh II.. MU Brno.
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Herman J.,Kučera R.,Šimša J. (1997). Metody řešení matematických úloh I.. MU Brno.
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