Abstract
Let R be a commutative ring with identity and let P be a proper ideal of R. The notion of weakly prime (resp., weakly semiprime) ideals are introduced by Anderson-Smith (resp., by Badawi), and considered a generalization of prime (resp., semiprime) ideals. An ideal P is called weakly prime (resp., weakly semiprime) if 0 ≠ ab ∈ P implies a ∈ P or b ∈ P (resp., 0 ≠ a2 ∈ P implies a ∈ P). The aim of this paper is to describe the weakly prime and weakly semiprime ideals in trivial ring extensions. Also, we introduce and study the weak Krull dimension of ring.
| Original language | English |
|---|---|
| Pages (from-to) | 307-314 |
| Number of pages | 8 |
| Journal | Moroccan Journal of Algebra and Geometry with Applications |
| Volume | 2 |
| Issue number | 2 |
| State | Published - Dec 2023 |
Bibliographical note
Publisher Copyright:© 2023, Sidi Mohamed Ben Abdellah University. All rights reserved.
Keywords
- decomposable ring
- trivial ring extension
- weak Krull dimension
- Weakly prime
ASJC Scopus subject areas
- Algebra and Number Theory