MT5868 Advanced Ring Theory

Academic year

2025 to 2026 Semester 1

Further information on which modules are specific to your programme.

Key module information

SCOTCAT credits

15

The Scottish Credit Accumulation and Transfer (SCOTCAT) system allows credits gained in Scotland to be transferred between institutions. The number of credits associated with a module gives an indication of the amount of learning effort required by the learner. European Credit Transfer System (ECTS) credits are half the value of SCOTCAT credits.

SCQF level

SCQF level 11

The Scottish Credit and Qualifications Framework (SCQF) provides an indication of the complexity of award qualifications and associated learning and operates on an ascending numeric scale from Levels 1-12 with SCQF Level 10 equating to a Scottish undergraduate Honours degree.

Planned timetable

11.00 am Mon (weeks 2, 4, 7, 9, 11), Tue & Thu

This information is given as indicative. Timetable may change at short notice depending on room availability.

Module coordinator

Dr Y Len

Dr Y Len
This information is given as indicative. Staff involved in a module may change at short notice depending on availability and circumstances.

Module Staff

Dr Yoav Len

This information is given as indicative. Staff involved in a module may change at short notice depending on availability and circumstances.

Module description

We will build on the foundations laid in MT3505 to study the structure of rings, modules (ring-theoretic analogues of vector spaces), and ideals. The theory of rings is the basis for many modern areas of maths such as algebraic geometry, number theory, representation theory, and homological algebra. For instance, geometric properties such as dimension and smoothness may be recast in terms of ideals in polynomial rings, and classifying representations of a group G by matrices over a field K may be interpreted as classifying modules over the group ring K[G]. The module will cover important topics in both commutative and non-commutative ring theory, and will include Hilbert's basis theorem, Nullstellensatz, and Wedderburn-Artin theorem.

Relationship to other modules

Pre-requisites

BEFORE TAKING THIS MODULE YOU MUST PASS MT3505

Assessment pattern

2-hour Written Examination = 100%

Re-assessment

Oral examination = 100%

Learning and teaching methods and delivery

Weekly contact

2.5 lectures (x 10 weeks), 1 tutorial (x 10 weeks)

Scheduled learning hours

35

The number of compulsory student:staff contact hours over the period of the module.

Guided independent study hours

116

The number of hours that students are expected to invest in independent study over the period of the module.

Intended learning outcomes

  • Demonstrate an understanding of the key concepts of ring theory, such as modules, ideals, polynomial rings, Noetherian and Artinian rings, radicals, and semisimple rings.
  • Produce coherent theoretical arguments (proofs) which establish general properties of rings and modules.
  • Understand the key structural concepts such as being Noetherian, Artinian or semisimple, and be able to determine whether particular rings have these properties.
  • Be able to state and use some the key theorems in advanced ring theory, such as Hilbert's basis theorem, Nullstellensatz, and Wedderburn-Artin theorem.
  • Appreciate the fundamental link between geometry and algebra via solution sets of polynomial equations.
  • Be able to use their knowledge to engage in creative problem-solving involving the above concepts.