Introduction to Commutative Algebra
- Learn proofs of fundamental theorems of commutative algebra.
- Understand relations between commutative algebra and other areas of mathematics, such as algebraic geometry and algebraic number theory.
- Apply theorems to provide proofs of statements about commutative rings and modules over them (problem solving).
- Apply knowledge of commutative algebra to analyze examples of particular rings and modules, for example given in terms of generators and relations.
- At the end of the course students are expected to be able to state fundamental theorems of commutative algebra, provide proofs and apply the theorems to solve problems and analyze examples.
- Ideals and radicals
- Modules over commutative rings
- Chain conditions for rings and modules
- Primary decomposition
- Integral extensions
- Dimension theory
- Discrete valuation rings and Dedekind rings
- Interim assessment (2 module)0.4 * Final exam + 0.3 * Midterm exam + 0.15 * Participation in the tutorial + 0.15 * Tests
- Atiyah, M. F., & Macdonald, I. G. (1969). Introduction To Commutative Algebra. Reading, Mass: CRC Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=421131
- Atiyah, M. F., & Macdonald, I. G. (2016). Introduction To Commutative Algebra, Student Economy Edition (Vol. Student economy edition). Boca Raton, FL: CRC Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1802204
- Altman, A., & Kleiman, S. (2013). A term of Commutative Algebra. United States, North America: Worldwide Center of Mathematics. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsbas&AN=edsbas.55CA89AB