Artins Algebra
1
Matrices
1.1
Basic Operations
2
Group Theory
2.1
Laws of Compositions
2.2
Groups and Subgroups
2.3
Subgroups of the Additive Group of Integers
2.4
Cyclic Groups
2.5
Homomorphisms
2.6
Isomorphisms
2.7
Equivalence Relations and Partitions
2.7.1
The Equivalence Relation Defined by a Map
2.8
Cosets
2.9
Modular Arithmetic
2.10
The Correspondence Theorem
2.10.1
PROBLEM
2.10.2
Problem
2.10.3
Problem
2.11
Product Groups
2.12
Quotient Groups
3
Vector Space
3.1
Subspace of
\(\mathbb{R}^n\)
3.2
Fields
3.3
Vector Spaces
4
Exercises
4.1
Chapter 1
4.2
Chapter 2
4.2.1
Laws of composition
4.2.2
Groups and Subgroups
4.2.3
Subgroups of the Additive Group of Integers
4.2.4
Cyclic group
4.2.5
Homomorphisms
4.2.6
Isomorphisms
4.2.7
Equivalence Relations and Partitions
4.2.8
Cosets
4.2.9
Modular Arthmetic
4.2.10
The Correspondence Theorem
4.2.11
Product Group
4.2.12
Quotient Groups
4.2.13
Miscellaneous Problems
4.2.14
Problem
5
Tempoarray files for exercises
5.1
Chapter 3
5.1.1
Fields
5.1.2
VectorSpaces
5.1.3
Bases and Dimension
6
My note
6.1
Group
6.2
Subgroup
6.3
Lagrange’s Theorem
6.4
Group Homorphism
7
Vector spaces.
Property of Ashan Jaymal
Artin’s Algebra
Chapter 7
Vector spaces.