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Dergiler / International Electronic Journal of Algebra / 2026 / Volume: 37 Issue: 37

Rings in which every regular finitely generated ideal is $S$-finitely presented

Salah Eddine Mahdou(S. M. Ben Abdellah University)
Mohamed Chhiti(S. M. Ben Abdellah University)
Sayfa
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Yayın Tarihi
2025-01-14
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

The obtained results yield new examples of regular $S$-coherent rings that are not $S$-coherent.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this work, we introduce and explore a class of rings where every regular finitely generated ideal is $S$-finitely presented, called a regular $S$-coherent ring.
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Temel Bulgular & Veri:This concept represents a weaker version of the $S$-coherent ring property.
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Sonuç & Katkı:The obtained results yield new examples of regular $S$-coherent rings that are not $S$-coherent.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:$S$-coherence · $S$-finitely presented · $S$-finite

Abstract

In this work, we introduce and explore a class of rings where every regular finitely generated ideal is $S$-finitely presented, called a regular $S$-coherent ring. This concept represents a weaker version of the $S$-coherent ring property. It is shown that any $S$-coherent ring is inherently a regular $S$-coherent ring, and in the case of domains, the two properties are equivalent. We also investigate how this notion extends to different settings of commutative ring extensions, including direct products, trivial ring extensions, and the amalgamated duplication of a ring along an ideal. The obtained results yield new examples of regular $S$-coherent rings that are not $S$-coherent.

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Bu Makaleye Atıf Yap

Mahdou, S. E., Chhiti, M. (2025). Rings in which every regular finitely generated ideal is $S$-finitely presented. International Electronic Journal of Algebra, Volume: 37 Issue: 37. https://doi.org/10.24330/ieja.1575698

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