The concepts of cotype submodule and cotype dimension of a module are introduced, their basic properties are studied, and a characterization of the amply supplemented modules with finite cotype dimension is given.
conatural class cotype submodule cotype dimensionA. Alvarado-Garc´ıa, H. A. Rinc´on-Mej´ıa and J. R´ıos-Montes, On the lattices of natural and conatural classes in R-mod, Comm. Algebra, 29(2) (2001), 541A. Alvarado-Garc´ıa, H. A. Rinc´on-Mej´ıa and J. R´ıos-Montes, On some lattices of module classes, J. Algebra Appl., 5(1) (2006), 105-117.F. W. Anderson and K. R. Fuller, Rings and Categories of Modules, Second Edition, Springer-Verlag, 1992.J. Clark, C. Lomp, N. Vanaja, and R. Wisbauer, Lifting Modules. Supplements and Projectivity in Module Theory, Frontiers in Mathematics, Birkh¨auser Ver- lag, Basel, 2006.I. Crivei and S. Crivei, Associated classes of modules, Stud. Univ. Babe¸s-Bolyai Math., 54(2) (2009), 23-32.S. Crivei and B. Torrecillas, On some monic covers and epic envelopes, Arab. J. Sci. Eng. Sect. C, 33(2) (2008), 123-135.J. Dauns and Y. Zhou, Classes of Modules, Pure and Applied Mathematics (Boca Raton), 281. Chapman & Hall/CRC, Boca Raton, FL, 2006.F. Kasch, Modules and Rings, Academic Press Inc. (London) Ltd, 1982.A. I. Kashu, On natural classes of R-modules in the language of ring R, Bul. Acad. S¸tiinte Repub. Mold. Mat., 2(45) (2004), 95-101.A. I. Kashu, On the lattice of closed classes of modules, Bul. Acad. S¸tiinte Repub. Mold. Mat., 2(48) (2005), 43-50.A. I. Kashu, Natural classes and torsion free classes in categories of modules, Bul. Acad. S¸tiinte Repub. Mold. Mat., 3(52) (2006), 101-108.A. I. Kashu, On natural and conatural sets of left ideals of a ring, Bul. Acad. S¸tiinte Repub. Mold. Mat., 2(54) (2007), 25-32.D. Keskin, On lifting modules, Comm. Algebra, 28 (2000), 3427-3440.R. Wisbauer, Foundations of Module and Ring Theory: A handbook for study and research, Gordon and Breach Science Publishers, 1991.Y. Zhou, Decomposing modules into direct sums of submodules with types, J. Pure Appl. Algebra, 138 (1999), 83-97.Alejandro Alvarado-Garc´ıa, Hugo Alberto Rinc´on-Mej´ıa, Bertha Tom´e-Arreola Facultad de Ciencias Universidad Nacional Aut´onoma de M´exico Circuito Exterior, C.U. M´exico D.F. e-mails: alejandroalvaradogarcia@gmail.com (A. Alvarado) hurincon@gmail.com (H. Rinc´on) bta@hp.fciencias.unam.mx (B. Tom´e) Jos´e R´ıos-Montes Instituto de Matem´aticas Universidad Nacional Aut´onoma de M´exico ´ Area de la Investigaci´on Cient´ıfica Circuito Exterior, C.U. M´exico D.F. e-mail: jrios@matem.unam.mx