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## ON COMPLETELY PRIME SUBMODULES

#### David Ssevviiri [1]

##### 175 205

The formal study of completely prime modules was initiated by N. J. Groenewald and the current author in the paper: Completely prime submodules, Int. Electron. J. Algebra, 13(2013), 1–14. In this paper, the study of completely prime modules is continued. Firstly, the advantage completely prime modules have over prime modules is highlighted and different situations that lead to completely prime modules given. Later, emphasis is put on fully completely prime modules (i.e., modules whose all submodules are completely prime). For a fully completely prime left R-module M, if a, b ∈ R and m ∈ M, then abm = bam, am = a km for all positive integers k, and either am = abm or bm = abm. In the last section, two different torsion theories induced by the completely prime radical are given.
Domain, prime module, completely prime module, completely prime radical, torsion theory
Konular Matematik JA35CM23JB Makaleler Yazar: David Ssevviiri
 Bibtex @ { ieja266194, journal = {International Electronic Journal of Algebra}, issn = {1306-6048}, eissn = {1306-6048}, address = {Prof. Dr. Abdullah HARMANCI}, year = {2016}, volume = {19}, pages = {77 - 90}, doi = {10.24330/ieja.266194}, title = {ON COMPLETELY PRIME SUBMODULES}, key = {cite}, author = {Ssevviiri, David} } APA Ssevviiri, D . (2016). ON COMPLETELY PRIME SUBMODULES. International Electronic Journal of Algebra, 19 (19), 77-90. DOI: 10.24330/ieja.266194 MLA Ssevviiri, D . "ON COMPLETELY PRIME SUBMODULES". International Electronic Journal of Algebra 19 (2016): 77-90 Chicago Ssevviiri, D . "ON COMPLETELY PRIME SUBMODULES". International Electronic Journal of Algebra 19 (2016): 77-90 RIS TY - JOUR T1 - ON COMPLETELY PRIME SUBMODULES AU - David Ssevviiri Y1 - 2016 PY - 2016 N1 - doi: 10.24330/ieja.266194 DO - 10.24330/ieja.266194 T2 - International Electronic Journal of Algebra JF - Journal JO - JOR SP - 77 EP - 90 VL - 19 IS - 19 SN - 1306-6048-1306-6048 M3 - doi: 10.24330/ieja.266194 UR - http://dx.doi.org/10.24330/ieja.266194 Y2 - 2018 ER - EndNote %0 International Electronic Journal of Algebra ON COMPLETELY PRIME SUBMODULES %A David Ssevviiri %T ON COMPLETELY PRIME SUBMODULES %D 2016 %J International Electronic Journal of Algebra %P 1306-6048-1306-6048 %V 19 %N 19 %R doi: 10.24330/ieja.266194 %U 10.24330/ieja.266194 ISNAD Ssevviiri, David . "ON COMPLETELY PRIME SUBMODULES". International Electronic Journal of Algebra 19 / 19 (Haziran 2016): 77-90. http://dx.doi.org/10.24330/ieja.266194