Explores modules over a ring, injective morphisms, isomorphisms, and canonical groups.
Explores Dedekind rings, fractional ideals, integrally closed properties, prime ideal factorization, and the structure of fractional ideals as a commutative group.
Explores adelic number theory, emphasizing lattices, modules, linear combinations, and Z-linear properties.
Explores cohomology and the cross product, demonstrating its application in group actions like conjugation.
Covers affine algebraic sets, hypersurfaces, elliptic curves, ideals, and Noetherian rings in algebraic geometry.
