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## A CLASS OF RINGS FOR WHICH THE LATTICE OF PRERADICALS IS NOT A SET

#### Rogelio Fernández-Alonso [1] , Silvia Gavito [2] , Henry Chimal-Dzul [3]

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In this paper we define Z-coinitial rings, where Z is an integral domain, and prove some of their properties. In particular, we characterize commutative noetherian domains and discrete valuation domains which are Z-coinital. We define radical modules and radical rings, and we prove that every countable Z-coinitial and right hereditary ring is a right radical ring. We give some examples of rings satisfying these conditions. Finally, we prove that the lattice of preradicals of every right radical ring is not a set.
 Bibtex @ { ieja266312, journal = {International Electronic Journal of Algebra}, issn = {1306-6048}, eissn = {1306-6048}, address = {Prof. Dr. Abdullah HARMANCI}, year = {2011}, volume = {9}, pages = {38 - 60}, doi = {}, title = {A CLASS OF RINGS FOR WHICH THE LATTICE OF PRERADICALS IS NOT A SET}, key = {cite}, author = {Gavito, Silvia and Fernández-Alonso, Rogelio and Chimal-Dzul, Henry} } APA Fernández-Alonso, R , Gavito, S , Chimal-Dzul, H . (2011). A CLASS OF RINGS FOR WHICH THE LATTICE OF PRERADICALS IS NOT A SET. International Electronic Journal of Algebra, 9 (9), 38-60. Retrieved from http://dergipark.gov.tr/ieja/issue/25202/266312 MLA Fernández-Alonso, R , Gavito, S , Chimal-Dzul, H . "A CLASS OF RINGS FOR WHICH THE LATTICE OF PRERADICALS IS NOT A SET". International Electronic Journal of Algebra 9 (2011): 38-60 Chicago Fernández-Alonso, R , Gavito, S , Chimal-Dzul, H . "A CLASS OF RINGS FOR WHICH THE LATTICE OF PRERADICALS IS NOT A SET". International Electronic Journal of Algebra 9 (2011): 38-60 RIS TY - JOUR T1 - A CLASS OF RINGS FOR WHICH THE LATTICE OF PRERADICALS IS NOT A SET AU - Rogelio Fernández-Alonso , Silvia Gavito , Henry Chimal-Dzul Y1 - 2011 PY - 2011 N1 - DO - T2 - International Electronic Journal of Algebra JF - Journal JO - JOR SP - 38 EP - 60 VL - 9 IS - 9 SN - 1306-6048-1306-6048 M3 - UR - Y2 - 2019 ER - EndNote %0 International Electronic Journal of Algebra A CLASS OF RINGS FOR WHICH THE LATTICE OF PRERADICALS IS NOT A SET %A Rogelio Fernández-Alonso , Silvia Gavito , Henry Chimal-Dzul %T A CLASS OF RINGS FOR WHICH THE LATTICE OF PRERADICALS IS NOT A SET %D 2011 %J International Electronic Journal of Algebra %P 1306-6048-1306-6048 %V 9 %N 9 %R %U ISNAD Fernández-Alonso, Rogelio , Gavito, Silvia , Chimal-Dzul, Henry . "A CLASS OF RINGS FOR WHICH THE LATTICE OF PRERADICALS IS NOT A SET". International Electronic Journal of Algebra 9 / 9 (Haziran 2011): 38-60.