Explores modules over a ring, injective morphisms, isomorphisms, and canonical groups.
Covers the concept of localization in algebra, focusing on making a ring multiplicative closed.
Explores Dedekind rings, fractional ideals, integrally closed properties, prime ideal factorization, and the structure of fractional ideals as a commutative group.
Explores Wedderburn's theorem, group algebras, and Maschke's theorem in the context of finite dimensional simple algebras and their endomorphisms.
Covers affine algebraic sets, hypersurfaces, elliptic curves, ideals, and Noetherian rings in algebraic geometry.
Explores adelic number theory, emphasizing lattices, modules, linear combinations, and Z-linear properties.
