On the ideal structure of semitrivial extensions

In this thesis, we aim to describe the structure of ideals of a particular ring extension, called semitrivial extension, and how they relate to the ideals of the base ring R. Semitrivial extensions arise as a generalization of Nagata’s idealization of a module M whenever a suitable morphism M ⊗ M → R is given, allowing to define a concept of multiplication among elements of M.