| 释义 |
prime element A non-zero element p in a commutative ring is said to be prime if whenever p divides the product ab, then p divides a or p divides b (or both). Thus, prime elements are, in a sense, atomic with regard to multiplication. 6 is not prime as it divides 4×9 without dividing 4 or 9. With the existence of units in rings, this definition of being prime generalizes better to rings than the notion of being divisible by itself and 1 only. Equivalently, the ideal (p) is a prime ideal if and only if p is a prime element. Compare irreducible.
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