**Abstract Algebra**

**Abstract algebra (also known as modern algebra) is the study of algebraic structures. Algebraic structures include groups, rings, fields, modules, vector spaces, lattices, and algebras.**

**In an introductory course on abstract algebra and its application, one may teach the following topics:**

**Definition of binary operations****Definition of semigroups, monoids, and groups****Subgroups****Normal subgroups and quotient groups****Group homomorphisms****Automorphisms****Cayley's theorem****Sylow's theorems****Definition of rings****Ring homomorphisms****Ideals and quotient rings****Prime and maximal ideals of rings****The field of quotients of an integral domain****Euclidean rings****Polynomial and formal power series rings**

For more details, refer to the following book:

Herstein, I. N. (2006). Topics in algebra. John Wiley & Sons.

**For applications of abstract algebra, one may choose some topics from the following general themes:**

**Coding Theory****Cryptography**

For more details, refer to the following book:

Lidl, R., Pilz, G. (2012). Applied Abstract Algebra. Springer Science & Business Media.

See also the following pages: