2024/2025
Некоммутативная алгебра 2
Статус:
Дисциплина общефакультетского пула
Кто читает:
Факультет математики
Где читается:
Факультет математики
Когда читается:
3, 4 модуль
Охват аудитории:
для всех кампусов НИУ ВШЭ
Преподаватели:
Ровинский Марат Зефирович
Язык:
английский
Кредиты:
6
Course Syllabus
Abstract
Associative rings and modules over them appear naturally in all domains of Mathematics. The goal of this course is to present some basic results on rings and modules, as well as to discuss several interesting examples and applications.
Course Contents
- Basic notions and examples of rings and modules
- Simple modules and Schur’s lemma
- Semisimple modules and Jacobson’s density theorem
- Artinian and noetherian conditions
- Jordan – Hölder theorem
- Krull – Remak – Schmidt theorem
- Applications to the Galois (and non – Galois) theory
- Wedderburn – Artin theorem
- Applications to the representation theory of finite groups
- Categories of modules and their equivalences
- Simple and semisimple rings and Brauer groups
Interim Assessment
- 2024/2025 4th modulemin[10,20/3((ratio of solved problem of the problem sets) + (ratio of solved problem of the final exam))]. A half-integer grade is rounded to the bigger nearest integer, another fractional grade is rounded to the nearest integer
