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 ...

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 ...

Abstract In this paper we devote to generalizing some results of componentwise linear modules over a polynomial ring to the ones over a Koszul algebra. Among other things, we show that the i-linear ...

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 ...