lie over
Word Rarity
Uncommon
Frequency: Zipf frequency 4.82 in modern English
10
Scrabble Score
7
Letters
1
Syllables
6
Unique Chars
Meaning
verb
Of a prime ideal q of a ring R' with subring R, to intersect with R at some other prime ideal p; q lies over p if and only if q∩R=p.
Transitive verb
Example Sentences
- "Let R be a subring of a ring R′ which is integral over R. If P is a prime ideal of R, then there is a prime ideal P′ of R′ that lies over P. Moreover, if P′ and P″ are prime ideals of R′ that lie over P and if P′ ⊆ P″, then P′ = P″."
- "Let R ⊆ S be integral domains such that R is integrally closed and S is integral over R. Suppose that P′ ⊆ P are prime ideals of R. Let Q be a prime ideal of S which lies over P. Then Q contains a prime ideal Q′ of S that lies over P′."