Polynomials on a Field: Properties and Applications

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Polynomials: Rings and Operations

Covers the basics of polynomials, focusing on rings, operations, and properties.

Ring Operations: Ideals and Classes

Covers the operations in rings, ideals, classes, and quotient rings.

Principal Ideal Domains: Structure and Homomorphisms

Covers the concepts of ideals, principal ideal domains, and ring homomorphisms.

Field Properties: Irreducibility and Units

Covers the properties of fields, including irreducibility and units in polynomials.

Rings and Fields: Principal Ideals and Ring Homomorphisms

Covers principal ideals, ring homomorphisms, and more in commutative rings and fields.

Polynomials: Definitions and Operations

Covers the definition and operations of polynomials, including addition and multiplication, degree, coefficients, and their role in algebraic systems.

Ring Structure: Polynomials and Coefficients

Covers the ring structure, focusing on polynomials and coefficients, including associativity, distributivity, and the product of rings.

Dimension theory of rings

Covers the dimension theory of rings, including additivity of dimension and height, Krull's Hauptidealsatz, and the height of general complete intersections.

Congruence Relations in Rings

Explores congruence relations in rings, principal ideals, ring homomorphisms, and the characteristic of rings.

Ideals in Commutative Rings

Covers the concept of ideals in commutative rings and their role in ring homomorphisms.