The prototype example is the ring of integers with the two operations of addition and multiplication. The rational, real and complex numbers are commutative rings of a type called fields. An algebra over a ring is itself a ring.

- Definitions and basic concepts,
- Homomorphisms, Homomorphism theorems,
- Polynomial rings,
- Unique factorization domain,
- Factorization theory,
- Euclidean domains,
- Arithmetic in Euclidean domains,
- Extension fields,
- Algebraic and transcendental elements,
- Simple extension,
- Introduction to Galois theory.

- A first course in abstract algebra byCall Number: 512.02 FRAISBN: 9789332519039Publication Date: 2003

- Series in Algebra : Rings Related to Stable Range Conditionsby Chen, Huanyin

Date Published: 2011 - Dolciani Mathematical Expositions : Guide to Groups, Rings, and Fieldsby GouvĂȘa, Fernando

Brilleslyper, - Introduction to Algebraby Cameron, Peter J.

Date Published: 2007