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 ...

Before reading this guide, you may find it helpful to read the guide on graphs from Module 7 (M7) and the guide on indices from Module 8 (M8). In Module 7 (M7) Graphs, you learned that simultaneous ...

Let p be a prime number and let GLn be the group of all invertible matrices over the prime field Fp. It is known that every irreducible GLn- module can occur as a submodule of P, the polynomial ...