We introduce and study the concept of α-short modules (a 0-short module is just a short module, i.e., for each submodule N of a module M, either N or $\frac{\mathrm{M}}{\mathrm{N}}$ is Noetherian).

This module shows how to develop an interactive multiplication program for students. Subsequetnly, the program will allow students to enhance multiplication skills for multiplying numbers under 100.

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 ...