# isomorphism

• Mar 8th 2010, 11:36 AM
empressA
isomorphism
Show that S={0, 4, 8, 12, 16, 20, 24} is a subring of Z28. Then prove that the map of f:Z7 onto S is given by f([x]7)=[8x]28 is an isomorphism.

I understand the subring part of the statement and have already proved that. But I do not understand how to prove the second statement.
• Mar 8th 2010, 03:38 PM
Drexel28
Quote:

Originally Posted by empressA
Show that S={0, 4, 8, 12, 16, 20, 24} is a subring of Z28. Then prove that the map of f:Z7 onto S is given by f([x]7)=[8x]28 is an isomorphism.

I understand the subring part of the statement and have already proved that. But I do not understand how to prove the second statement.

Prove that it is a bijective mapping which is a ring homomorphism ( $f(xy)=f(x)f(y),\text{ }f(x+y)=f(x)+f(y)$)
• Mar 10th 2010, 09:50 AM
empressA
Thank you..i understand what you are saying and I got it..