Noncommutative Algebra

3-0-9 units · Graduate

Topics may include Wedderburn theory and structure of Artinian rings, Morita equivalence and elements of category theory, localization and Goldie's theorem, central simple algebras and the Brauer group, representations, polynomial identity rings, invariant theory growth of algebras, Gelfand-Kirillov dimension.

Spring 2023

Noncommutative algebra studies algebraic phenomena involving multiplication for which commutativity law fails, such as product of matrices in linear algebra; such phenomena arise in various disciplines ranging from quantum physics to number theory.

Readings

There is no required textbook. A full set of lecture notes is provided. Possible other references include the following: ↗
Listed reading
Cohn, P. M. 2003. Further Algebra and Applications . London: Springer. ISBN: 9781852336677 See chapters 2, 4, 5, 7, 8. An earlier edition of basically the same text as volumes 2, 3 of the series Algebra by the same author. The author of the recommended textbook is Professor Paul Moritz Cohn (1924 -2006) of University College, London. He was born in Hamburg, Germany to a Jewish family which was later persecuted by the Nazis and perished in Holocaust. Paul Cohn himself was saved by Kindertransport, an organised rescue effort for children of persecuted Jewish families that helped them emigrate to the United Kingdom. ↗
Listed reading
Weibel, Charles A. 1994. An Introduction to Homological Algebra . Cambridge England: Cambridge University Press. ISBN: 9780521559874 ↗
Listed reading

Prerequisites & course information

Prereq: 18.702 Acad Year 2027-2028: G (Spring) Acad Year 2028-2029: Not offered 3-0-9 units

Sources

Course catalogue ↗2026–2027
MIT OpenCourseWare ↗Spring 2023
MIT OCW syllabus ↗
Historical MIT OpenCourseWare offering. Named reading entries and schedule topics are automatically extracted from the linked source pages.