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Ring Theory

The study of rings: sets with addition and multiplication, from the integers to polynomial and matrix rings.

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A non-Noetherian local ring with finitely generated maximal ideal

2026NotesBogdan Zavyalov

A complete local ring with a finitely generated maximal ideal is Noetherian. Drop completeness and it fails: an ultraproduct construction gives a non-Noetherian local ring whose maximal ideal is principal.

Алгебра 1. Лекция 2. Многочлены и конечные поля

2026OtherAlexey Ilyin

Алгебра 1. Лекция 3. Конечные поля и гауссовы числа

2026LectureAlexey Ilyin

Лекция 5. Идеалы, теорема о гомоморфизмах, евклидовы и факториальные кольца.

2026LectureAlexey Ilyin

Алгебра 1, Листок 1

2026Problem sheetAlexey Ilyin

Задачные листки к курсам алгебры. Институт и учебное заведение в исходных публикациях не указаны, поэтому здесь не названы.