Factorisation in PIDsCovers factorisation in PIDs, prime ideals, unique tuples, and common prime factors.
Chinese Remainder TheoremExplores the Chinese remainder theorem in commutative rings and ideals, demonstrating its applications and relevance in finding unique solutions.
Localization and IdealsCovers the concept of localization and ideals in rings, focusing on extended and contracted ideals, integral extensions, and monic equations.
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.
Module over a RingExplores modules over a ring, injective morphisms, isomorphisms, and canonical groups.
