primary ideal

noun1

1. •
   Given a commutative ring R, any ideal I such that for any a,b ∈ R, if ab ∈ I then either b ∈ I or aⁿ ∈ I for some integer n > 0.

   • The prime and primary ideals play roles which are (very roughly) similar to those played by prime numbers and by prime.power numbers in elementary arithmetic. — 1953