Subject Code: MA3L307 Subject Name: RINGS AND FIELDS L-T-P: 3-1-0 Credit: 4
Pre-requisite(s): None
 
Unit I. Definition, examples and properties of rings, Subrings, Ideals, Prime and maximal ideals, Ring homomorphism, Isomorphism theorems.
Unit II. Quotient Rings, Rings of fractions, Chinese Remainder Theorem, Polynomial Rings, Integral domain, Euclidean Domain, Principal Ideal Domain, Unique Factorization Domain, Gauss’ Lemma, Irreducibility criterion, Eisenstein’s criterion,
Unit III. Definition, examples and properties of fields, Characteristic of a field, Field extensions, Algebraic and transcendental elements.
Unit IV. Splitting fields, Separable and normal extensions, Primitive roots of unity, Cyclotomic polynomials, Finite fields.

Text/Reference Books:
  1. J. A. Gallian, Contemporary Abstract Algebra, Boston, Houghton-Mufflin, 2002.
  2. D. S. Dummit, R. M. Foote, Abstract Algebra, Wiley-India Edition, 2013.
  3. M. Artin, Algebra, Pearson Education, 2011.
  4. I. N. Herstein, Topics in Algebra, New York: Wiley, 1975.
  5. C. Musili, Introduction to rings and modules, Narosa Publishing House, 1994.