Affine Algebraic SetsCovers affine algebraic sets, hypersurfaces, elliptic curves, ideals, and Noetherian rings in algebraic geometry.
Factorisation in PIDsCovers factorisation in PIDs, prime ideals, unique tuples, and common prime factors.
Dimension of Algebraic VarietyExplores the dimension of algebraic varieties, including the (Krull)-dimension of rings and computing dimensions using tools from commutative algebra.
Group Algebra: Maschke's TheoremExplores Wedderburn's theorem, group algebras, and Maschke's theorem in the context of finite dimensional simple algebras and their endomorphisms.
