Module classes and the lifting property

Let R be a ring. A collection of R-modules containing the zero module and closed under isomorphisms will be denoted by X. An R-module M is said to be X-lifting if for every X-submodule N of M there exists A \leq N such that M=A \oplus B and N \cap B is small in B [11]. In the present paper, we consider the question: Can we characterize X-lifting modules via objects of the class X?

Anahtar Kelimeler:

Lifting module, torsion theory

Module classes and the lifting property

Keywords:

Lifting module, torsion theory,

PDF

___

Alkan, M.: On τ -lifting modules and τ -semiperfect modules. Turkish J. Math. 33, 117-130 (2009).
Al-Khazzi, I, Smith, P.F.: Classes of modules with many direct summands. J. Aust. Math. Soc., Ser. A. 59(1), 19 (1995).
Anderson, F.W., Fuller, K.R.: Rings and Categories of Modules. Springer-Verlag, New York 1974.
Crivei, S.: Relatively lifting modules. Algebra Colloq., to appear. Dogruoz, S., Smith, P.F.: Modules which are extending relative to module classes. Comm. Algebra, 26(6), 1699- (1998).
Dogruoz, S., Smith, P.F.: Quasi-continuous modules relative to module classes. Vietnam J. Math. 27(3), 241-251 (1999).
Dogruoz, S., Smith, P.F.: Modules which are weak extending relative to module classes. Acta Math. Hung. 87, 10 (2000).
Golan, J.S.: Torsion Theories. Pitmann Mon.and Surveys in Pure and Appl.Math. 29, 1986.
Ko¸san, T., Harmanci, A.: Modules supplemented relative to a torsion theory. Turkish J. Math. 28(2), 177-184 (2004).
Ko¸san, M.T., Harmanci, A.: Decompositions of modules supplemented relative to a torsion theory. International J. Math. 16(1), 43-52 (2005).
Ko¸san, M.T., Harmanci, A.: Modules which are lifting relative to module classes. Kyungpook J. Math. 48(1), 71 (2008).
Mohammed, S.H., M¨uller, B.J.: Continous and Discrete Modules. London Math. Soc., LN 147, Cambridge Univ.Press, 1990.
Smith, P.F., Viola-Prioli, A.M., Viola-Prioli, J.: Modules complemented with respect to a torsion theory. Comm. Algebra 25, 1307- 1326 (1997).
Stentr¨om, B.: Rings of quotients, Springer, Berlin, 1975.
Xu, J.: Flat covers of modules, Lecture Notes in Math., Springer, Berlin, 1996.
Muhammet Tamer KOS¸AN Department of Mathematics, Gebze Institute of Technology C¸ ayırova Campus 41400 Gebze, Kocaeli-TURKEY e-mail: mtkosan@gyte.edu.tr