MA 5070: Modules and Fields
All the updates related to MA 5070 are announced here.
Class timings: Tuesday, Wednesday, and Friday (12:00noon-13:00) & Room No. B-109
Examination and Grades:
The grades will be decided by the marks obtained in the assignments, mid-term, surprise tests, the final examination, and also by the performance in the class.
Syllabus:
Review of Rings, Modules, Cartesian products and direct sums of modules, Free modules, Quotient modules, Simple and semi-simple modules, Isomorphism theorems.
Modules over principal ideal domains and applications. Noetherian and Artinian rings/Modules, Hilbert basis theorem. Jordan-Holder theorem.
Field extensions. Algebraic/Transcendental elements, Algebraic extensions, Algebraic closure of a field and Uniqueness, Finite fields, Cyclotomic fields,
Splitting field of a polynomial, Separable, Purely inseparable extensions, Normal extensions, Primitive elements, Simple extensions. Fundamental theorem of Galois theory, Solvability by radicals.
References:
- D. S. Dummit and R. M. Foote, Abstract Algebra, John Wiley & Sons Inc, 3rd Edition, 2004.
- C. Musili, Introduction to Rings and Modules, Narosa Publishing House, New Delhi 1994.
- S. Lang, Algebra, 3rd Edition, Springer-Verlag (India), 2004.