• Modules of homomorphisms, injective and projective modules, tensor product and flat modules.
• Prime and maximal ideals in a ring, operation over ideals. Chinese remainder theorem, nilradical and Jacobon’s radical; divisibility in a ring, factorial ring, primary ideals and primary decomposition.
• rings and modules of fractions. Ideals in a ring of fractions, local ring.
• Integral and almost integral elements over a ring. Integrally closed and almost integrally closed rings, Dedekind rings, fractional ideals, ideals classes.