0

Can anyone tell me the application of module . I know they are used in representation theory . What are there other places where the modules are used ???

Om Prakash
  • 160
  • Welcome to Maths SX! In algebraic geometry, in analytic geometry and in number theory, for instance. – Bernard Sep 27 '19 at 12:15
  • @Bernard how ?? – Om Prakash Sep 27 '19 at 12:16
  • Modules can show up in the abstract construction of tensor fields in differential geometry. For a smooth manifold, the set of vector fields $\mathcal{X}(M)$ is a module over the ring $C^{\infty}(M)$ of infinitely differentiable functions. One can see tensor fields as elements of the tensor $\mathcal{X}(M) \otimes \mathcal{X}(M)$.

    See also, this: https://en.wikipedia.org/wiki/Tensor_field#The_C%E2%88%9E(M)_module_explanation

     – Diego Marcon Sep 27 '19 at 12:34
  • Algebraic and analytic geometries, among many other things, consider sheaves of modules (e.g. modules of differentials). As to nimber theorem, you have the ideal class group of a ring of integers. – Bernard Sep 27 '19 at 12:34

0 Answers0