RETRACTED: On Nil and Nilpotent Rings and Modules

DOI: 10.4236/ajcm.2017.73027   PDF   HTML     647 Downloads   1,231 Views  


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This article has been retracted to straighten the academic record. In making this decision the Editorial Board follows COPE's Retraction Guidelines. The aim is to promote the circulation of scientific research by offering an ideal research publication platform with due consideration of internationally accepted standards on publication ethics. The Editorial Board would like to extend its sincere apologies for any inconvenience this retraction may have caused.


Editor guiding this retraction: Prof. Hari M. Srivastava (EiC, AJCM)


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[1] Van Lint, J.H. (1982) Introduction to Coding Theory. Springer Verlag, New York.
[2] Kothe, G. (1930) Die Struktur der Rings, deren Restklassenring nach dem Radikal vollstanding reduzibelist. Mathematische Zeitschrift, 32, 161-186.
[3] Amitsur, S.A. (1956) Redicals of Polynomial Rings. Canadian Journal of Mathematics, 8, 335-361.
[4] Amitsur, S.A. (1973) Nil Radicals, Historical Notes and Some New Results. In: Rings, Modules and Radicals, (Proceedings International Colloquium, Keszthely, 1971), Colloquium Mathematical Society Janos Bolyai, 6, 47-65.
[5] Jespers, E., Krempa, J. and Puczylowski, E.R. (1982) On Radicals of Graded Rings, Communications in Algebra, 10, 1849-1854.
[6] Smoktunowicz, A. (2013) A Note on Nil and Jacobson Radicals in Graded Rings. Journal of Algebra and Its Applications, 2, 1-10.
[7] Puczylowski, E.R. (1993) Some Questions Concerning Radicals of Associative Rings. In: Theory of Radicals, Colloquia Mathematics Societatis Janos Bolyai, 61, 209-227.
[8] Puczylowski, E.R. (2006) Questions Related to Koethe’s Nil Ideal Problem. In: Algebra and Its Applications, Contemporary Mathematics, Vol. 419, American Mathematics Society, 269-283.
[9] Passman, D.S. (2004) A Course in Ring Theory, AMS Chelsea Publishing, Amer. Math. Society-Providence, Rhode Island.
[10] Ali, M.M. (2008) Idempotent and Nilpotent Submodules of Multiplication Modules. Communications in Algebra, 36, 4620-4642.
[11] Chebotar, M.A., Lee, P.H. and Puczylowski, E.R. (2010) On Andrunakievich’s Chain and Koethe’s Problem. Israel Journal of Mathematics, 180, 119-128.
[12] Klein, A.A. (2005) Annihilators of Nilpotent Elements. International Journal of Mathematics and Mathematical Sciences, 21, 3517-3519.
[13] Sanh, N.V., Vu, N.A., Ahmed, K.F.U., Asawasamrit, S. and Thao, L.P. (2010) Primeness in Module Category. Asian-European Journal of Mathematics, 3, 151-160.
[14] Ahmed, K.F.U., Thao, L.P. and Sanh, N.V. (2013) On Semi-Prime Modules with Chain Conditions. East-West Journal of Mathematics, 15, 135-151.
[15] Sanh, N.V., Asawasamrit, S., Ahmed, K.F.U. and Thao, L.P. (2011) On Prime and Semiprime Goldie Modules. East-West Journal of Mathematics, 4, 321-334.
[16] Kasch, F. (1982) Modules and Ring. London Mathematical Society Monograph, 17, Academic Press, London, New York, Paris.
[17] Stenstrom, B. (1975) Rings of Quotients. Springer-Verlag, Berlin, Heidelberg, New York.
[18] Musili, C. (2006) Introduction to Rings and Modules. Narosa Publishing House, New Delhi.

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