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.
https://www.isibang.ac.in/~adean/infsys/database/Bmath/RM.html
- Teacher: Sayan Pal
- Teacher: Maneesh Thakur