MAT 495 - Abstract Algebra |
| Course Detail: |
Sets and Equivalence Relations, Semigroups & Monoids, Free Semigroup & Free Monoid, Congruence Relations and Quotient Structures, Fundamental Theorem of Semigroup Homomorphism, Groups, Sn, Zn, Subgroups, Normal Subgroups, Cayley?s Theorem, Lagrange?s Theorem, Quotient Group, Cyclic Subgroups, Generating Sets, Generators, Fundamental Theorem of group Homomorphism, Rings and Ideals, Fundamental Theorem of Ring Homomorphism, Integral Domain, Principal Ideal Domain, Divisibility in Integral Domain, Unique Factorization Domain, Field, K[t]- the polynomials over a field K, K[t] as a Principal Ideal Domain and Unique Factorization Domain, Fundamental Theorem of Algebra, Ordered Sets and Lattices, Principle of Duality, Bounded Lattices, Distributive Lattices, Complemented Lattices, Boolean Algebra as a Bounded, Distributive and Complemented Lattice.
[Pre-requisite: MAT 250 ]
[Credit Hours: 3] |
