Course Archives Theoretical Statistics and Mathematics Unit

Course: Rings and Modules Instructor: Maneesh Thakur Room: G26 Level: Undergraduate Time: Currently offered

Syllabus Past Exams Syllabus: i) Rings, Left and Right ideals, Examples of Polynomial rings, Matrix rings and Group rings, Quotient rings by two-sided ideals. ii) Commutative rings: Units, Nilpotents, Adjunction of elements, Chinese remainder theorem, Maximal and prime ideals, Localization. iii) Factorisation theory in domains: Irreducible and prime elements, Euclidean domains, Principal Ideal Domains, Unique Factorisation Domains, Gausss lemma, Eisensteins Criterion. iv) Noetherian rings, Hilbert basis theorem. v) Modules: Structure of finitely generated modules over a PID and their representation matrices, Applications to Rational canonical form and Jordan form of a matrix. Reference Texts: (a) M. Artin: Algebra. (b) S. D. Dummit and M. R. Foote: Abstract Algebra. (c) I. N. Herstein: Topics in Algebra. (d) K. Hoffman and R. Kunze: Linear Algebra. (e) C. Musili: Rings and Modules. (f) J. A. Gallian: Contemporary Abstract Algebra. (g) N. Jacobson: Basic Algebra. Evaluation: Mid-term 30 marks Assignment 20 marks Final Exam 50 marks Total 100 marks Top of the page Past Exams

Midterm 23.pdf 24.pdf Semestral 23.pdf Supplementary and Back Paper 23.pdf Top of the page

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