Math Is Fun Forum

Suppose

and

are positive integer numbers with

, then show that the mapping

with

is isomorphism ring!

Let

be a ring with unity and let

be the ring of endomorphisms of

. Let

, and let

be given by

.
a) Show that

is an endomorphism of

b) Show that

is a subring of

c) Prove the analogue of Cayley's theorem for

by showing that

of (b) is isomorphic to

Let

be a commutative ring and

be the ideal of

. Show that

is also the ideal of

.

Please give me EXAMPLE and explain about:

- Commutative ring and uncommutative ring which doesn't have unit element
- Ring which has different unit element with its subring's unit element

If

is continuous, and

Find the maximum value of

Please explain to me...