Homological algebra and module theory constitute a vibrant area of contemporary mathematics, interweaving concepts from algebra, topology and geometry. At its core, homological algebra studies chain ...

In this paper we show that the Rees algebra can be made into a functor on modules over a ring in a way that extends its classical definition for ideals. The Rees algebra of a module M may be computed ...

In this note we give the description of a morphism related with the structure of the canonocal module of the Rees algebra R(I) of an ideal I in a local ring. As an application we obtain Ikeda's ...

Before reading this guide, it may be helpful to read the guide from Module 7 (M7) about proportion and variation. Module 7 (M7) proportion and variation is concerned with direct proportion between two ...

Before you start, it may be helpful to read the guides on coordinates and graphs from Module 2 (M2) and Module 3 (M3). When two lines are perpendicular, the product of their gradients is 1. Lines A ...