I’m aware that not all commutative rings guarantee the existence of gcd’s. The only example I have of this currently is the ring of even integers in which 2 has no divisors and therefore no greatest common divisor. I can’t, however, think of a commutative ring with identity in which this is the case. I know that such an example would need to not be a UFD since UFD’s guarantee the existence of gcd’s. Any ideas?
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26 commutative rings with identity that aren’t gcd domains. And 5 of them are domains if that matters to you. – rschwieb Jul 04 '18 at 13:12
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1Thanks, that's useful. – Anonymous Jul 05 '18 at 05:26
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No problem! Glad it is useful. – rschwieb Jul 05 '18 at 13:33