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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
We study inclusions between the first two and the last two classes of simple modules in terms of some associated radicals and proper classes.
📌 3 Key Takeaways
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Objective & Hypothesis:For a unitary right module $M$, there are two known partitions of simple modules in the category $\sigma[M]$: the first one divides them into $M$-injective modules and $M$-small modules, while the second one divides them into $M$-projective modules and $M$-singular modules.
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Key Findings & Data:For a unitary right module $M$, there are two known partitions of simple modules in the category $\sigma[M]$: the first one divides them into $M$-injective modules and $M$-small modules, while the second one divides them into $M$-projective modules and $M$-singular modules.
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Conclusion & Impact:We study inclusions between the first two and the last two classes of simple modules in terms of some associated radicals and proper classes.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Radical · Proper class · Simple module
Abstract
For a unitary right module $M$, there are two known partitions of simple modules in the category $\sigma[M]$: the first one divides them into $M$-injective modules and $M$-small modules, while the second one divides them into $M$-projective modules and $M$-singular modules. We study inclusions between the first two and the last two classes of simple modules in terms of some associated radicals and proper classes.
Keywords
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Cite This Article
Crivei, S., Tütüncü, D. K. (2017). On some radicals and proper classes associated to simple modules. Journal of Algebra Combinatorics Discrete Structures and Applications, Cilt: 4 Sayı: 2 (Special Issue: Noncommutative rings and their applications), 123–129. https://doi.org/10.13069/jacodesmath.284943