Ring theory MOC

Prime element

Let be a ring. A nonzero element is prime iff it is not a unit and it satisfies Euclid’s lemma: ring Whenever for then or .

This is one way to generalize the Prime number to an arbitrary ring.¹

Properties

• All primes are irreducible in an integral domain

See also

• Prime ideal

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Footnotes

1. 2022. Algebraic number theory course notes, §1.1, p. 1 ↩