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 ...

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 ...

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 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 ...

The same method is used for adding and subtracting numerical fractions or algebraic fractions. Find a common denominator Write each fraction as an equivalent fraction with that common denominator ...