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Journals / International Electronic Journal of Algebra / 2026 / Volume: 15 Issue: 15

ON THE LEVITZKI RADICAL OF MODULES

Nico J. Groenewald
David Ssevviiri
Pages
—
Publication Date
2014-06-01
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AI Summary & Key Takeaways

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⚡ TL;DR(Too Long; Didn't Read)

Lastly, we show that the class of all l-prime modules RM with RM 6= 0 forms a special class of modules.

📌 3 Key Takeaways

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Objective & Hypothesis:In [1] a Levitzki module which we here call an l-prime module was introduced.
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Key Findings & Data:We define the Levitzki radical of an R-module M as L(M) = l.√0.
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Conclusion & Impact:Lastly, we show that the class of all l-prime modules RM with RM 6= 0 forms a special class of modules.
🔬Design:Article
📍Scope:Comprehensive Sample
⚙️Variables:l-prime submodule · semi l-prime · s-prime submodule

Abstract

In [1] a Levitzki module which we here call an l-prime module was introduced. In this paper we define and characterize l-prime submodules. Let N be a submodule of an R-module M. If l.√N := {m ∈ M : every l- system of M containingm meets N}, we show that l.√N coincides with the intersection L(N) of all l-prime submodules of M containing N. We define the Levitzki radical of an R-module M as L(M) = l.√0. Let β(M), U(M) and Rad(M) be the prime radical, upper nil radical and Jacobson radical of M respectively. In general β(M) ⊆ L(M) ⊆ U(M) ⊆ Rad(M). If R is commutative, β(M) = L(M) = U(M) and if R is left Artinian, β(M) = L(M) = U(M) = Rad(M). Lastly, we show that the class of all l-prime modules RM with RM 6= 0 forms a special class of modules.

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Cite This Article

Groenewald, N. J., Ssevviiri, D. (2014). ON THE LEVITZKI RADICAL OF MODULES. International Electronic Journal of Algebra, Volume: 15 Issue: 15. https://doi.org/10.24330/ieja.266239

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