Courses :: Module, COMMUTATIVE ALGEBRA

	Overview
	Noetherian rings and modules, Hilbert's Nullstellensatz, affine algebraic varieties, dimension theory of commutative rings including Krull's Principal Ideal Theorem, localization and its applications, regular rings and nonsingularity. Possible additional topics: completion, projective varieties and graded rings and modules, Hilbert functions, projective and invertible modules.

Overview

Noetherian rings and modules, Hilbert's Nullstellensatz, affine algebraic varieties, dimension theory of commutative rings including Krull's Principal Ideal Theorem, localization and its applications, regular rings and nonsingularity.
Possible additional topics: completion, projective varieties and graded rings and modules, Hilbert functions, projective and invertible modules.

	Learning Outcomes
	On successful completion of the module, students should be able to: State some of the classical theorems of commutative algebra. Prove any of the theorems given in the course. Deduce properties which follow from these theorems. Prove other algebraic results using rigorous arguments.

Learning Outcomes

	Autumn Supplementals/Resits
	No autumn repeat.

Autumn Supplementals/Resits

	Timetable
	This timetable is not currently available, please contact the Mathematics And Statistics Department.

Timetable

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COMMUTATIVE ALGEBRA