SubjectsSubjects(version: 953)
Course, academic year 2023/2024
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Commutative Rings - NMAG301
Title: Komutativní okruhy
Guaranteed by: Department of Algebra (32-KA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2021
Semester: winter
E-Credits: 6
Hours per week, examination: winter s.:3/1, C+Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: not taught
Language: Czech
Teaching methods: full-time
Teaching methods: full-time
Additional information: https://www2.karlin.mff.cuni.cz/~stanovsk/vyuka/komutalg.htm
Guarantor: doc. RNDr. David Stanovský, Ph.D.
Class: M Bc. MMIB
M Bc. MMIB > Povinné
M Bc. MMIT
M Bc. MMIT > Povinné
M Bc. OM
M Bc. OM > Zaměření MSTR
M Bc. OM > Povinně volitelné
Classification: Mathematics > Algebra
Incompatibility : NMAG305
Interchangeability : NMAG305
Is incompatible with: NMAG305
Is interchangeable with: NMAG305
In complex pre-requisite: NMAG349
Annotation -
A recommended course for Information Security and specialization Mathematical Structures within General Mathematics. It covers basic topics of commutative ring theory.
Last update: G_M (15.05.2012)
Course completion requirements -

Students have to solve 3 series of homeworks.

Last update: Stanovský David, doc. RNDr., Ph.D. (28.09.2020)
Literature -
Fundamental sources: Other books:
  • M. F. Atiah, I.G. Macdonald, Introduction to Commutative Algebra, Addison Wesley, 1969.
  • H. Matsumura, Commutative Ring Theory, W. A. Benjamin, 1970.
  • P. Samuel, O. Zariski, Commutative Algebra vol. I and II, Princeton, D. Van Nostrand Company, 1958, 1960.
  • R. Y. Sharp, Steps in Commutative Algebra (London Math. Society Student Text), Cambridge Univ. Press, 2nd ed., 2001.
Last update: Stanovský David, doc. RNDr., Ph.D. (28.09.2020)
Requirements to the exam -

Students have to pass final exam. The requirements for the exam correspond to what has been done during lectures and practicals.

Last update: Stanovský David, doc. RNDr., Ph.D. (28.09.2020)
Syllabus -

Fundamentals - ideals, radical, notherian property, chinese remainder theorem

Galois theory - splitting fields, algebraic closure, Galois correspondence

Introduction to algebraic geometry - the IV correspondence, Hilbert's Nullstellensatz, irreducible decomposition

Introduction to algebraic number theory - integral extensions, Dedekind domains

Last update: Stanovský David, doc. RNDr., Ph.D. (28.09.2020)
 
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