Journal article
Weakly prime ideals
Houston Journal of Mathematics, Vol.29(4), pp.831-840
2003
Abstract
Let R be a commutative ring with identity. We define a proper ideal P of R to be weakly prime if 0 ≠ ab ∈ P implies a ∈ P or b ∈ P. For example, every proper ideal of a quasilocal ring (R, M) with M2 = 0 is weakly prime. We show that a weakly prime ideal P that is not prime satisfies P2 = 0, in fact, P√0 = 0. A number of results concerning weakly prime ideals and examples of weakly prime ideals are given. We show that every proper (principal) ideal of R is a product of weakly prime ideals if and only if R is a finite direct product of Dedekind domains (π-domains) and SPIR's or (R, M) is a quasilocal ring with M2 = 0.
Details
- Title: Subtitle
- Weakly prime ideals
- Creators
- D.D. AndersonE. Smith
- Resource Type
- Journal article
- Publication Details
- Houston Journal of Mathematics, Vol.29(4), pp.831-840
- ISSN
- 0362-1588
- Language
- English
- Date published
- 2003
- Academic Unit
- Mathematics
- Record Identifier
- 9984230419402771
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