Fermat's Equation: Integral Solutions and Gaussian Integers

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Covers the ring of polynomials, focusing on coefficients and multiplication.

Explores algebraic structures of morphism spaces, including stability properties and injective ring homomorphisms.

Explores division rings, integral domains, fields, and ideals in rings, with examples and key theorems.

Explores cyclotomic extensions, prime numbers, and ideal norms in number theory.

Explores the additivity of dimension and height in a finitely generated k-algebra domain, showcasing its applications and implications.

Covers integers, rings, subrings, invertibility, divisors of zero, and equivalence relations in formal fractions.

Covers commutative ring morphisms, subrings, and injective ring morphisms.

Introduces sub-rings and morphisms in ring theory, emphasizing stability by multiplication.

Explores factorisation in Principal Ideal Domains and the properties of prime numbers.

Introduces the definition and examples of A-modules, including sub-modules and ideals.