Let be the ring of matrixes with elements from the ring . the set of matrixes in which all elements below the diagonal are 0. the set of matrixes with the elements in the principal diagonal are 0. the set of diagonal matrixes.
Let be the ring of matrixes with elements from the ring . the set of matrixes in which all elements below the diagonal are 0. the set of matrixes with the elements in the principal diagonal are 0. the set of diagonal matrixes.
Prove that,
I do it for it will be clear.
Define the mapping
Then the kernel of this mapping ( ) is and range is .