Elements of a Ring: R Has 64 Elements

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SUMMARY

The discussion confirms that if a ring homomorphism f: R->S has a kernel with 4 elements and an image with 16 elements, then the ring R must contain 64 elements. This conclusion is derived from the formula |Im(f)| = |R|/|ker(f)|, leading to |R| = 4 * 16 = 64. The logic presented is validated by participants in the discussion.

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AkilMAI
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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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James said:
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.
 

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