Arab Journal of Basic and Applied Sciences· 2026Q2
Prime graphs of a seminearring
- 0citations
- Q2SCImago
- 2026year
Short summary
This paper introduces and explores the 'completely equiprime graph' of a seminearring, demonstrating that elements of a strong ideal form a clique within this new graph structure.
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Key points
- Introduces the concept of a completely equiprime graph for seminearrings.
- Demonstrates that elements of a strong ideal form a clique in the c-e-prime graph.
- Proves that the diameter of the equiprime graph is less than 4 when restricted to a strong ideal.
AI-generated from the title and abstract; the full text is not read.
Abstract
A graph that successfully handles both binary operations of the underlying algebraic structure is essential. This work continues to explore the equiprime graph of a seminearring, a concept that is recently introduced in the field, and provides results on minimal edge coverings and investigates the conditions under which various prime graphs coincide. Further, we demonstrate that if we limit the vertex set of the equiprime graph to [Formula: see text] where L is a strong ideal, the diameter of the equiprime graph will be strictly less than 4. Additionally, we define the concept of a completely equiprime graph of a seminearring and prove relevant results. We also show that the elements of a strong ideal induce a clique in the c-e-prime graph.
The authors' abstract, as published at the source. Arab Journal of Basic and Applied Sciences, 2026 · DOI ↗
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Field: Algebra and Number Theory
Algebra and Number TheoryMathematics