ADVANCED ALGEBRA
Direct product of groups (external and internal), Isomorphism theorems, Diamond isomorphism theorem, Butterfly lemma, Conjugate classes.
Commutators, Derived subgroups, Normal series and solvable groups, Composition series, Refinement theorem and Jordan-Holder theorem for infinite groups.
Modules, Submodules, Quotient modules, Direct sums and module homomorphisms, Generation of modules, Cyclic modules.
Field theory: Extension fields, Algebraic and transcendental extensions, Separable and inseparable extensions, Normal extensions, Splitting fields.
Galois theory: Elements of Galois theory, Fundamental theorem of Galois theory, Solvability by radicals.
- Dileep S. Chauhan and K.N. Singh, Studies in Algebra, JPH, Jaipur, 2011.
- P.B. Bhattacharya, S.K. Jain, S.R. Nagpaul, Basic Abstract Algebra, Cambridge University Press, 1995.
- I.N. Herstein, Topics in Algebra, Wiley Eastern Ltd., New Delhi, 1975.
- Knapp, W. Anthony, Advanced Algebra, Springer, 2008.
1. Deepak Chatterjee, Abstract Algebra, PHI. Ltd. New Delhi, 2015.
2. John B. Fraleigh, A First Course in Abstract Algebra, Narosa Publishing House, New Delhi, 2002.
3. S. David, Richard M. Foote Dummit, Abstract Algebra, John Wiely & Sons Inc. USA, 2003.
4. S. Hang, Algebra, Addison Wesley, 1993.
5. N. Jacobson, Basic Algebra, Hindustan Publishing Co, 1988.
6. M. Artin, Algebra, Prentice Hall India, 1991.
7. C. Musili, Introduction to Rings and Modules, Narosa Publishing House, New Delhi, 1994.
