MU25005 Basic Commutative Algebra

Mathematical Institute in Opava
Winter 2019
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Michal Marvan, CSc. (lecturer)
doc. RNDr. Michal Marvan, CSc. (seminar tutor)
Guaranteed by
doc. RNDr. Michal Marvan, CSc.
Mathematical Institute in Opava
Prerequisites (in Czech)
TYP_STUDIA(N)
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Syllabus
  • - Rings, subrings, ideals, quotient rings.
    - Basics of divisibility theory, integral domains, Euclidean rings, principal ideal rings, Gaussian rings, division rings, resultant and discriminant.
    - Basics of homological algebras, modules, exact sequences, direct sums, tensor products, free, projective and injective modules, complexes, homology, resolvents, Ext functors.
    - Fields, number fields, algebraic and transcendental extensions, algebraic numbers, basics of classical Galois theory.
Literature
    recommended literature
  • S. Mac Lane. Homology. Springer, Berlin, 1963. info
  • G. Birkhoff, S. Mac Lane. A Survey of Modern Algebra. Macmillan, 1953. info
Language of instruction
Czech
Further Comments
Study Materials
The course can also be completed outside the examination period.
The course is also listed under the following terms Winter 2012, Winter 2013, Winter 2014, Winter 2015, Winter 2016, Winter 2017, Winter 2018.
  • Enrolment Statistics (recent)
  • Permalink: https://is.slu.cz/course/sumu/winter2019/MU25005