Course Archives Theoretical Statistics and Mathematics Unit | ||||||||
Course: Rings and Modules Instructor: Maneesh Thakur Room: G26 Level: Undergraduate Time: Currently offered |
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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:
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Midterm
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