ABSTRACT
ALGEBRA

Structure & Symmetry

Visualizing Direct Product:

C_{12} \times C_8

(G, \bullet)

Groups

Reversible structure, symmetry, rotations, reflections, and composition.

\phi(xy)=\phi(x)\phi(y)

Homomorphisms and other structure-preserving translations between algebraic systems.

Planned

Mod 03

(R, +, \bullet)

Arithmetic

Sets with compatible addition and multiplication operations.

\mathbb{F} = R / M

Rings where nonzero elements support division, providing the scalars of linear algebra.

Planned

Mod 05

V \text{ over } \mathbb{F}

Linearity

Abelian groups equipped with scalar multiplication over a field.

Planned

Mod 06

\text{Gal}(E/F)

Unification

The bridge between group structure and field extensions.