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Y by
In general, is a ring. A ring is and integral domain iff is the only zero-divisor. Another way of putting this is for some prime number show that,
where where . Consider for some where is still some prime number. This implies although by definition ONLY for some this implies that either or although in modulus we have thus or must be a zero-divisor thus we can conclude that for any given prime is an integral domain. Consider if we have that implies that , in this case, or where is equal to the other that implies that is a zero divisor and if is non-prime that implies that for some non- divisor, is a zero divisor.
where where . Consider for some where is still some prime number. This implies although by definition ONLY for some this implies that either or although in modulus we have thus or must be a zero-divisor thus we can conclude that for any given prime is an integral domain. Consider if we have that implies that , in this case, or where is equal to the other that implies that is a zero divisor and if is non-prime that implies that for some non- divisor, is a zero divisor.
This post has been edited 3 times. Last edited by Thayaden, Nov 7, 2024, 6:51 PM