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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 40 Issue: 4

X-GORENSTEIN PROJECTIVE AND Y-GORENSTEIN INJECTIVE MODULES

Fanyun Meng
Qunxing Pan
Pages
—
Publication Date
2011-04-01
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

We show that the principal results on Gorenstein modules remain true for X-Gorenstein projective right R-modules, Y-Gorenstein injective right R-modules and Y-Gorenstein flat left R-modules.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Let X be a class of right R-modules that contains all projective right R-modules.
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Key Findings & Data:Ouarghi (X-Gorenstein projective modules, International Mathematical Forum 5 (10), 487–491, 2010).
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Conclusion & Impact:We show that the principal results on Gorenstein modules remain true for X-Gorenstein projective right R-modules, Y-Gorenstein injective right R-modules and Y-Gorenstein flat left R-modules.
🔬Design:Research Article
📍Scope:2010 Verileri
⚙️Variables:X-Gorenstein projective modules · Y-Gorenstein injective modules · Y-Gorenstein flat modules

Abstract

Let X be a class of right R-modules that contains all projective right R-modules. The notion of X-Gorenstein projective modules was introduced by D. Bennis and K. Ouarghi (X-Gorenstein projective modules, International Mathematical Forum 5 (10), 487–491, 2010). In this paper, we introduce Y-Gorenstein injective right R-modules and Y-Gorenstein flat left R-modules, where Y is a class of right R-modules that contains all injective right R-modules. We show that the principal results on Gorenstein modules remain true for X-Gorenstein projective right R-modules, Y-Gorenstein injective right R-modules and Y-Gorenstein flat left R-modules.

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Cite This Article

Meng, F., Pan, Q. (2011). X-GORENSTEIN PROJECTIVE AND Y-GORENSTEIN INJECTIVE MODULES. Hacettepe Journal of Mathematics and Statistics, Volume: 40 Issue: 4. https://ajindex.com/articles/1403618

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