# Elements of a ring

#### James

##### New member
f:R->S is a homomorphism of rings,such that kernel of f has 4 elements and the image of f has 16.How many elements has R?
16=|Im ( f )|=|R/ker f|=|R|/|ker f|=|R|/4=>|R|=4*16=64
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#### Swlabr

##### New member
f:R->S is a homomorphism of rings,such that kernel of f has 4 elements and the image of f has 16.How many elements has R?
16=|Im ( f )|=|R/ker f|=|R|/|ker f|=|R|/4=>|R|=4*16=64
Yes, your logic and answer are both correct.