primary ideal

Noun

 * 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.
 * 2) * 1970 [Frederick Ungar Publishing], John R. Schulenberger (translator),, Algebra, Volume 2, 1991, Springer, page 189,
 * Thus all higher primary ideals are symbolic powers of higher prime ideals.
 * Prüfer has called the ideals a with the property a* = a v-ideals. The integral v-ideals are just those in whose primary ideal decomposition only higher primary ideals occur.
 * Prüfer has called the ideals a with the property a* = a v-ideals. The integral v-ideals are just those in whose primary ideal decomposition only higher primary ideals occur.

Translations

 * German: primäres Ideal