ALGEBRA 2

On successful completion of this course, students will be able to: - describe the group of symmetry and isometry, direct product of groups and the symmetric group with the proof of the Cayley theorem - examine the structure of a ring in detail and define subrings, ideals, maximal and prime, quotient rings and direct products of rings - prove the Fundamental theorem on homomorphisms of rings, the first and second theorem of isomorphisms of rings with applications - define the characteristic of a ring and prove basic theorems related to it - describe the fraction field - describe the ring of polynomials and polynomial functions and prove the basic theorems about the factorization of polynomials with applications - describe the construction of field extensions and Euclidean rings, especially the Euclid’s algorithm of dividing with residue with applications