- About Us
- About University
- Double degree programmes
- Learning Page
- Courses
- Faculty of Computer Science and Cybernetics
- Faculty of Economics
- Faculty of Geography
- Faculty of History
- Faculty of Information Technology
- Faculty of Law
- Faculty of Mechanics and Mathematics
- Faculty of Physics
- Faculty of Psychology
- Faculty of Sociology
- Institute of Geology
- Institute of High Technologies
- Institute of International Relations
- Institute of Journalism
- Institute of Philology
- Military Institute
- Philosophical Faculty

- Regulations
- Contacts

# Algebraic structures of modern mathematics

Descipline | Algebraic structures of modern mathematics |

Faculty | Faculty of Mechanics and Mathematics |

Faculty URL | http://www.mechmat.univ.kiev.ua/en |

Language | English |

Degree | Doctorat (Ph.D.) |

Credits | 4 |

Semester | 3 |

Description | The sets, relations of order and equivalence ratio. Cardinal numbers, well-order, Zorn`s Lemma. Groups, cyclic groups, normal subgroups, quotient groups. Abelian groups, groups of substitutions, matrix groups. Presentation of a group generative and correlations. Rings, ideals and homorphism theory of divisibility, Euclid and factorial rings. Artin and Noether ring noncommutative ring. Fields expanding fields splitting field, algebraic and transcendental extension fields. Galois Theory. Algebra, algebra ideals factor. Nilpotent Lie algebra theorem Engel. Solvable Lie algebra theorem Lee. Finite simple Lie algebra over the field C classification. |

Teachers | Bondarenko E.V. Department of algebra and mathematical logic, Faculty of Mechanics and Mathematics, Phone: +380442590517 e-mail: ievgbond@gmail.com |