Year 2014, Volume 15, Issue 15, Pages 77 - 89 2014-06-01

ON THE LEVITZKI RADICAL OF MODULES

Nico J. Groenewald [1] , David Ssevviiri [2]

209 251

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.
l-prime submodule, semi l-prime, s-prime submodule, upper nil radical, Levitzki radical
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  • Department of Mathematics and Applied Mathematics Nelson Mandela Metropolitan University Port Elizabeth South Africa e-mail: nico.groenewald@nmmu.ac.za David Ssevviiri Department of Mathematics and Applied Mathematics Nelson Mandela Metropolitan University Port Elizabeth South Africa e-mail: david.ssevviiri@nmmu.ac.za
Other ID JA38AY84SV
Journal Section Articles
Authors

Author: Nico J. Groenewald

Author: David Ssevviiri

Bibtex @ { ieja266239, journal = {International Electronic Journal of Algebra}, issn = {1306-6048}, eissn = {1306-6048}, address = {Abdullah HARMANCI}, year = {2014}, pages = {77 - 89}, doi = {10.24330/ieja.266239}, title = {ON THE LEVITZKI RADICAL OF MODULES}, key = {cite}, author = {Groenewald, Nico J. and Ssevviiri, David} }
APA Groenewald, N , Ssevviiri, D . (2014). ON THE LEVITZKI RADICAL OF MODULES. International Electronic Journal of Algebra, 15 (15), 77-89. DOI: 10.24330/ieja.266239
MLA Groenewald, N , Ssevviiri, D . "ON THE LEVITZKI RADICAL OF MODULES". International Electronic Journal of Algebra 15 (2014): 77-89 <http://dergipark.org.tr/ieja/article/266239>
Chicago Groenewald, N , Ssevviiri, D . "ON THE LEVITZKI RADICAL OF MODULES". International Electronic Journal of Algebra 15 (2014): 77-89
RIS TY - JOUR T1 - ON THE LEVITZKI RADICAL OF MODULES AU - Nico J. Groenewald , David Ssevviiri Y1 - 2014 PY - 2014 N1 - doi: 10.24330/ieja.266239 DO - 10.24330/ieja.266239 T2 - International Electronic Journal of Algebra JF - Journal JO - JOR SP - 77 EP - 89 VL - 15 IS - 15 SN - 1306-6048-1306-6048 M3 - doi: 10.24330/ieja.266239 UR - https://doi.org/10.24330/ieja.266239 Y2 - 2019 ER -
EndNote %0 International Electronic Journal of Algebra ON THE LEVITZKI RADICAL OF MODULES %A Nico J. Groenewald , David Ssevviiri %T ON THE LEVITZKI RADICAL OF MODULES %D 2014 %J International Electronic Journal of Algebra %P 1306-6048-1306-6048 %V 15 %N 15 %R doi: 10.24330/ieja.266239 %U 10.24330/ieja.266239
ISNAD Groenewald, Nico J. , Ssevviiri, David . "ON THE LEVITZKI RADICAL OF MODULES". International Electronic Journal of Algebra 15 / 15 (June 2014): 77-89. https://doi.org/10.24330/ieja.266239