Abstract Algebra : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : :

Abstract algebra is the study of structures in mathematics. The following algebraic structures are studied in this chapter: groups, rings, subrings and ideals, fields, polynomial rings, and Boolean algebra. Vector spaces over fields, linear mappings, structure of finite fields, roots of unity in finite field, elliptic curves, and hyperelliptic curves are also studied. Some number-theoretic concepts are also generalized and extended in this chapter.