Another counting principle – Sylow’s theorem
Euclidean rings – A particular Euclidean ring – Polynomial rings – Polynomials over the rational field
Extension Fields – Roots of polynomials.
Elements of Galois Theory.
Canonical forms: Triangular form – Trace and Transpose – Hermitian, unitary and normal Transformations.
Reference Book:
1. A First Course in Abstract Algebra by J.B.Fraleigh, Narosa Publishing House, New Delhi, 1988. 2. Algebra by M.Artin, Edition 2, Pearson’s Education, Prentice-Hall, 2011.
Text Book:
Topics in Algebra by I.N.Herstein (II Edition). Unit I: Chapter 2 – Sections: 2.11 to 2.12. Unit II: Chapter 3 – Sections: 3.7 to 3.10. Unit III: Chapter 5 – Sections: 5.1, 5.3. Unit IV: Chapter 5 – Section: 5.6. Unit V: Chapter 6 – Sections: 6.4, 6.8 and 6.10.
