Module MAU34102: Commutative Algebra
- Credit weighting (ECTS)
- 5 credits
- Semester/term taught
- Hilary Term 2019-20
- Contact Hours
- 11 weeks, 3 lectures including tutorials per week
- Lecturer
- Prof. Sergey Mozgovoy
- Learning Outcomes
- Module Content
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- Exact sequences and tensor products of modules.
- Rings of fractions.
- Noetherian and Artinian rings, Hilbert's basis theorem, primary decomposition.
- Integral dependence, Noether's normalization theorem, Hilbert's Nullstellensatz.
- Valuation theory: Discrete valuation rings, Dedekind domains, p-adic numbers, Hensel's lemma.
- Dimension theory.
- Module Prerequisite
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MAU22102
- Required Reading
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- Atiyah and Macdonald. Introduction to commutative algebra.
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- Zariski and Samuel. Commutative algebra, Vol. I and II.
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- Eisenbud. Commutative algebra.
- Assessment Detail
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This module will be examined in a 2 hour examination in Trinity term. Continuous assessment will contribute 15% to the final grade for the module at the annual examination session. Re-assessments if required will consist of 100% exam.