examples of modules
This entry is a of examples of modules over rings. Unless otherwise specified in the example, will be a module over a ring .
If is a subring of a ring , then is an -module, with action given by multiplication in .
If is any ring, then any (left) ideal of is a (left) -module, with action given by the multiplication in .
Let and let . Then is a module over the ring of integers. Further, define the sets and and . Then , , and are modules over , with action given by if even if the product is redefined as and , but now the identity element is . However by our new product definition even if , the ring identity element originally In the more general definition of module which does not require an identity element in the ring and does not require for all , we observe that in this example just constructed. (one of the purposes of this comment is to show that all modules need not be unital ones).
Yetter-Drinfel’d module. (http://planetmath.org/QuantumDouble)
|Title||examples of modules|
|Date of creation||2013-03-22 14:36:28|
|Last modified on||2013-03-22 14:36:28|
|Last modified by||mathcam (2727)|