素そ元げん

noun

prime element

Technical term in abstract algebra, specifically ring theory. A prime element is a nonzero, non-unit element p such that whenever p divides a product ab, p divides a or p divides b.

• 整せい数すう環かんにおいて、素そ数すうは素そ元げんである。

  In the ring of integers, prime numbers are prime elements.

• 素そ元げん分ぶん解かい整せい域いきでは、すべての既き約やく元げんが素そ元げんとは限かぎらない。

  In a unique factorization domain, not every irreducible element is necessarily a prime element.