MODERN ALGEBRA

Code: MA222 | L-T-P-C: 3-0-0-6

Sets, relations, mappings, equivalence relations, binary operations, monoids, semi-groups; Groups, subgroups, cyclic groups, order of an element, cosets, Lagrange's theorem, normal subgroups, quotient groups, homomorphisms, automorphsims, permutation groups, Cayley's theorem, conjugacy, class equation, Cauchy's theorem, Sylow's theorems.

Rings, ideals, quotient rings, integral domains, fields, maximal ideals, prime ideals, irreducible elements, prime elements, Euclidean domains, principal ideal domains, unique factorization domains.

Fields, characteristic of a field, prime subfield, field extensions, algebraic extensions, separable extensions, finite fields, algebraically closed field, algebraic closure of a field.

Texts:

1. J. A. Gallian, Contemporary Abstract Algebra, 4th Edition, Narosa, 1998.
2. I. N. Herstein, Topics in Algebra, Wiley, 2004.
3. P. B. Bhattacharya, S. K. Jain and S. R. Nagpaul, Basic Abstract Algebra, Cambridge University Press, 1995.

References:

1. D. S. Dummit and R. M. Foot, Abstract Algebra, 2nd Edition, John Wiley, 1999.
2. J. B. Fraleigh, A First Course in Abstract Algebra, Addison Wesley, 2002.
3. M. Artin, Algebra, Prentice Hall of India, 1991.