Question

show that the range of a homomorphism is a submodule​

Answer 1

Answer:

Step-by-step explanation:

h(u*v)=h(u).h(v)

Answer 2

The range of a homomorphism is a sub-module:

• Let R be a ring and let M be an R-module. An R-module of M is an abelian subgroup W such that for all r@R, all w@W.
• For example, let R act on itself by left multiplication. The R-sub-modules of R are precisely the left ideals of R.
• Let M be an R-module

       1. Let {Ma} be any collection of sub-modules of M. Then Ma is sub-module

          M.

      2. Let Mn be an increasing sequence of sub-modules of M. Then Mn is a

           sub-module of M.

      3. Let A and B be two sub-modules of M. Then A+B= {a+b: a@A and b@B}

         is a sub-module of M.