surjective homomorphism between unitary rings
Proof. . In a ring, the identity element is unique, whence it suffices to show that has the properties required for the unity of the ring . When is an arbitrary element of this ring, there is by the surjectivity an element of such that . Thus we have
. Let be a unit of . Then
whence is a multiplicative inverse of .
|Title||surjective homomorphism between unitary rings|
|Date of creation||2013-03-22 19:10:22|
|Last modified on||2013-03-22 19:10:22|
|Last modified by||pahio (2872)|