The main objective of this course is to study the properties, behavior and relations of algebraic objects such as commutative rings and modules. Thus, the course prepares students for applications in algebraic geometry, cryptography, coding theory and number theory.

Rings and ring homomorhisms, Ideals and Quotient rings, Prime ideals, Maximal ideals, Nilpotent elements and Nil Radical, Jacobson radical, Operations on ideals, Modules and Quotient modules, Finitely generated modules, Rings and Modules with Ascending Chain Condition, Hilber Basis Theorem