Thread: 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.

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 ( )

Thank you..i understand what you are saying and I got it..