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 ...

One useful feature of the Python math module is quick access to mathematical constants. You can make Python more effective as ...

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 ...

The Virasoro vertex algebra arises as the symmetry algebra of a two-dimensional conformal field theory. The Virasoro irreducible modules are well-known, and they play a prominent role in rational ...

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 ...

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 ...

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 ...