query: Example of a ring satisfying Euclid's lemma, but with no gcd and/or lcm.
positive_passages.docid: 114480
positive_passages.text: Example of a domain where all irreducibles are primes and that is not a GCD domain
negative_passages.docid: 86724
negative_passages.text: Example of a non-zero module that has no associated primes
negative_passages.docid: 80616
negative_passages.text: A ring with few invertible elements
negative_passages.docid: 31263
negative_passages.text: Quotient rings of Gaussian integers
negative_passages.docid: 51593
negative_passages.text: Every finite commutative ring with no zero divisors contains a multiplicative identity?
negative_passages.docid: 116526
negative_passages.text: Finite ring has only zero divisors and units
negative_passages.docid: 45213
negative_passages.text: Easiest and most complex proof of $\gcd (a,b) \times \operatorname{lcm} (a,b) =ab.$
negative_passages.docid: 17059
negative_passages.text: A ring element with a left inverse but no right inverse?
negative_passages.docid: 114688
negative_passages.text: Show that a division ring is simple.
negative_passages.docid: 84751
negative_passages.text: How can it be possible to localize a ring at a set with zero divisors?
negative_passages.docid: 143051
negative_passages.text: Inverting noninvertible elements in a bigger ring.
negative_passages.docid: 95533
negative_passages.text: I need some help with a GCD and LCM's Problem
negative_passages.docid: 236
negative_passages.text: Proof of general Euclid's Lemma in a UFD (by Euclidean algorithm?)
negative_passages.docid: 63338
negative_passages.text: Noncommutative failure of IBN: $\,R^n\cong R^m \Rightarrow n - m,$ ring $R$ with maximal ideal $I$ such that $R/I$ is not a division ring?
negative_passages.docid: 4397
negative_passages.text: Finite rings without zero divisors are division rings.
negative_passages.docid: 69546
negative_passages.text: Example of non-commutative ring with exactly 2014 two sided-proper ideals.
negative_passages.docid: 37960
negative_passages.text: Zero Divisors in Direct Product of Rings