Localization and IdealsCovers the concept of localization and ideals in rings, focusing on extended and contracted ideals, integral extensions, and monic equations.
Dedekind Rings and Fractional IdealsExplores Dedekind rings, fractional ideals, integrally closed properties, prime ideal factorization, and the structure of fractional ideals as a commutative group.
Ideals and PPCMCovers the concept of ideals in polynomial rings and their properties.
Factorisation in PIDsCovers factorisation in PIDs, prime ideals, unique tuples, and common prime factors.
Fractions of RingsExplores the concept of fractions of rings and their uniqueness in ideals and quotients.