|
|
|
|
- Rings and Fields, Alexei Skorobogatov.
Contents: (52 pages)
1 Basic Properties Of Rings
2 Factorizing In Integral Domains
3 Euclidean domains and principal ideal domains
4 Homomorphisms and factor rings
5 Field extensions
6 Ruler and Compass Constructions
7 Finite fields
- Introduction to Rings & Fields, Stefan Waner
Contents: (32 pages)
1. Rings, Subrings and Homomorphisms
2. Units, Zero Divisors and Integral Domains
3. Fields
4. The Ring of Polynomials over a Field
5. A Result on Factorization of Polynomials over Q
6. Ideals
7. Maximal and Prime Ideals
8. Extension Fields
9. Vector Spaces
10. Theory of Algebraic Extensions
11 You Can't Trisect an Angle
12 Classification of Finite Fields
13 Existence of Algebraic Closure
14 Transcendence of e
- Symmetric Algebras over rings and fields, Thomas C. Craven, Tara L. Smith
Contents: (6 pages)
1 Introduction
2 Hyperplanes and ideals
3 Quotients of Algebras
References
- Rings and Fields
The operations of addition and multiplication in real numbers have direct parallels with operations which may be applied to pairs of integers, pairs of integers mod another positive integer, vectors in Rn , matrices mapping Rn to Rm , polynomials with real or integer coefficients, etc. The properties of the operations may be slightly different in each application, but there remains a subset of the properties of + and ·, (addition and multiplication), which are common to all these examples...
Contents: (9 pages)
1. Introduction to Rings
2. Examples of Rings
3. Properties of Rings
4. Integral Domains and Fields
5. Subrings and Ring Isomorphisms
6. Exercises
|
|
|
|
|
|
