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Since Charles has already given you an example, I'll just mention that there is a name for integral domains in which any two non-zero elements have a gcd: GCD-Domains.

See also Pete's response to “Counter”-example for Gauss’s Lemma on irreducible polynomials“Counter”-example for Gauss’s Lemma on irreducible polynomials.

Since Charles has already given you an example, I'll just mention that there is a name for integral domains in which any two non-zero elements have a gcd: GCD-Domains.

See also Pete's response to “Counter”-example for Gauss’s Lemma on irreducible polynomials.

Since Charles has already given you an example, I'll just mention that there is a name for integral domains in which any two non-zero elements have a gcd: GCD-Domains.

See also Pete's response to “Counter”-example for Gauss’s Lemma on irreducible polynomials.

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user1073
user1073

Since Charles has already given you an example, I'll just mention that there is a name for integral domains in which any two non-zero elements have a gcd: GCD-Domains.

See also Pete's response to “Counter”-example for Gauss’s Lemma on irreducible polynomials.