Commutative Algebra

Subject 620-636 (2009)

Note: This is an archived Handbook entry from 2009. Search for this in the current handbook

Credit Points: 12.50
Level: 9 (Graduate/Postgraduate)
Dates & Locations:

This subject has the following teaching availabilities in 2009:

Semester 1, - Taught on campus.
Pre-teaching Period Start not applicable
Teaching Period not applicable
Assessment Period End not applicable
Last date to Self-Enrol not applicable
Census Date not applicable
Last date to Withdraw without fail not applicable


Timetable can be viewed here. For information about these dates, click here.
Time Commitment: Contact Hours: 36 hours comprising 2 one-hour lectures per week and 1 one-hour practice class per week.
Total Time Commitment: 3 contact hours plus 7 hours private study per week.
Prerequisites: None
Corequisites: None
Recommended Background Knowledge: It is recommended that students have completed a third year subject in algebra (equivalent to 620-321 [2008] Algebra).
Non Allowed Subjects: None
Core Participation Requirements: It is University policy to take all reasonable steps to minimise the impact of disability upon academic study and reasonable steps will be made to enhance a student's participation in the University's programs. Students who feel their disability may impact upon their participation are encouraged to discuss this with the subject coordinator and the Disability Liaison Unit.


Dr John Richard James Groves
Subject Overview: Commutative algebra is the basis of modern algebraic geometry. It provides the rigorous foundation for the study of curves and surfaces and their generalisations. Students will study: basic properties of rings, basic properties of modules including Nakayama's Lemma; Hom and tensor; Localisation; Noetherian properties and the Hilbert Basis theorem; Associated primes and primary decomposition; Grobner bases; Integral extensions; extension of primes in integral extensions; the Hilbert Nullstellensatz; Extended applications taken from Algebraic Geometry and Algebraic Number Theory.
Objectives: After completing this subject, students should gain:
- a deeper understanding of the theory of rings and modules;
- an understanding of the basic concepts of Commutative Algebra such as localisation, Noetherian, associated primes and integral extensions;
- an understanding of how these basic concepts apply in an area of mathematics other than algebra;
- an understanding of proof-producing skills in an algebraic context and to assist in refining the presentation of the consequent proofs;
- the ability to pursue further studies in this and related areas.
Assessment: Up to 60 pages of written assignments (75%: three assignments worth 25% each, due early, mid and late in semester), a 2 hour written examination (25%, in the examination period).
Prescribed Texts: TBA
Recommended Texts: TBA
Breadth Options:

This subject is not available as a breadth subject.

Fees Information: Subject EFTSL, Level, Discipline & Census Date
Generic Skills: Upon completion of this subject, students should gain the following generic skills:
- Problem-solving skills including the ability to engage with unfamiliar problems and identify relevant solution strategies
- Analytical skills through the ability to construct and express logical arguments and to work in abstract or general terms to increase the clarity and efficiency of analysis
- Through interactions with other students, the ability to work in a team
- Time management skills: the ability to meet regular deadlines while balancing competing commitments
Related Majors/Minors/Specialisations: R05 RM Master of Science - Mathematics and Statistics

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