___

• M. F. Atiyah and I. G. Macdonald, Introduction to Commutative Alge- bra, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1969.
• K. Brown, P. A. A. B. Carvalho and J. Matczuk, Simple modules and their essential extensions for skew polynomial rings, ArXiv e-prints, (2017), available at 1705.06596.
• P. A. A. B. Carvalho, C. Lomp and D. Pusat-Yilmaz, Injective modules over down-up algebras, Glasg. Math. J., 52(A) (2010), 53-59.
• P. A. A. B. Carvalho and I. M. Musson, Monolithic modules over Noetherian rings, Glasg. Math. J., 53(3) (2011), 683-692.
• P. A. A. B. Carvalho, C. Hatipoglu and C. Lomp, Injective hulls of simple modules over dierential operator rings, Comm. Algebra, 43(10) (2015), 4221- 4230.
• G. Cauchon, Anneaux de polyn^omes essentiellement bornes, Ring theory (Proc. Antwerp Conf. (NATO Adv. Study Inst.), Univ. Antwerp, Antwerp, 1978), Lecture Notes in Pure and Appl. Math., vol. 51, Dekker, New York, (1979), 27-42.
• I. S. Cohen, Commutative rings with restricted minimum condition, Duke Math. J., 17 (1950), 27-42.
• C. Hatipoglu, Stable torsion theories and the injective hulls of simple modules, Int. Electron. J. Algebra, 16 (2014), 89-98.
• C. Hatipoglu and C. Lomp, Injective hulls of simple modules over nite di- mensional nilpotent complex Lie superalgebras, J. Algebra, 361 (2012), 79-91.
• D. Hilbert, Ein Beitrag zur Theorie des Legendre'schen Polynoms, Acta Math., 18(1) (1894), 155-159.
• J. P. Jans, On co-Noetherian rings, J. London Math. Soc., 1(2) (1969), 588-590.
• A. V. Jategaonkar, Certain injectives are Artinian, Noncommutative ring the- ory (Internat. Conf., Kent State Univ., Kent Ohio, 1975), Lecture Notes in Math., Vol. 545, Springer, Berlin, (1976), 128-139.
• E. Matlis, Injective modules over Noetherian rings, Paci c J. Math., 8 (1958), 511-528.
• I. M. Musson, Finitely generated, non-Artinian monolithic modules, New trends in noncommutative algebra, Contemp. Math., 562, Amer. Math. Soc., Providence, RI, (2012), 211-220.
• A. Rosenberg and D. Zelinsky, Finiteness of the injective hull, Math. Z., 70 (1958/1959), 372-380.
• A. Sant'Ana and R. Vinciguerra, On cyclic essential extensions of simple modules over dierential operator rings, ArXiv e-prints, (2017), available at 1704.04970.
• W. Schelter, Essential extensions and intersection theorems, Proc. Amer. Math. Soc., 53(2) (1975), 328-330.
• D. W. Sharpe and P. Vamos, Injective Modules, Cambridge Tracts in Math- ematics and Mathematical Physics, No. 62, Cambridge University Press, London-New York, 1972.
• P. F. Smith, The Artin-Rees property, Paul Dubreil and Marie-Paule Malli- avin Algebra Seminar, 34th Year (Paris, 1981), Lecture Notes in Math., 924, Springer, Berlin-New York, (1982), 197-240.
• P. Vamos, The dual of the notion of \ nitely generated", J. London Math. Soc., 43 (1968), 643-646.