Explores the concept of fractions of rings and their uniqueness in ideals and quotients.
Explores Dedekind rings, fractional ideals, integrally closed properties, prime ideal factorization, and the structure of fractional ideals as a commutative group.
Covers factorisation in PIDs, prime ideals, unique tuples, and common prime factors.
Explores the Chinese remainder theorem in commutative rings and ideals, demonstrating its applications and relevance in finding unique solutions.
Covers the concept of localization and ideals in rings, focusing on extended and contracted ideals, integral extensions, and monic equations.
