We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Strongly prime ideals and strongly zero-dimensional rings.
- Authors
Gottlieb, Christian
- Abstract
A prime ideal is said to be strongly prime if whenever contains an intersection of ideals, contains one of the ideals in the intersection. A commutative ring with this property for every prime ideal is called strongly zero-dimensional. Some equivalent conditions are given and it is proved that a zero-dimensional ring is strongly zero-dimensional if and only if the ring is quasi-semi-local. A ring is called strongly -regular if in each ideal , there is an element such that for all . Connections between the concepts strongly zero-dimensional and strongly -regular are considered.
- Subjects
PRIME ideals; IDEALS (Algebra); MAXIMAL ideals; DIMENSIONAL analysis; DIMENSIONAL reduction algorithms
- Publication
Journal of Algebra & Its Applications, 2017, Vol 16, Issue 10, p-1
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498817501912