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Let be a commutative ring with identity
. If
is the ring of rational integers, then the map
![]() | (1) |
is a ring-homomorphism. Its kernel is a principal ideal , generated by an integer
. The canonical injective (one-to-one) homomorphism
is a ring-homomorphism between
and a subring of
.
If in addition, is an integral domain, then
is a prime ideal, and consequently either
or
for some prime number
.
Cite this web-page as:
Štefan Porubský: Prime ring.