Purely Lifting Module

Najmaddin H. Gareeb, Bahar H. Al-Bahraany

College of Science, University of Sulaimani

In this paper we will generalize the concept of a lifting module. various properties and characterizations of a general case; the pure lifting module, are established and some other known results has been generalized

Keywords: Pure and small sub-modules, Lifting, regular, hollow, multiplication, prime, faithful, and cancellation modules.

1. D. Keskin, on lifting modules, Comm. Algebra 2000, 28 (7), 3427-3440.
2. D.J. Fieldhouse, Pure Theories, Math. Ann. 1969, 184, 1-18.
3. Majid M. All and David J. Smith, Pure Submodules of Multiplication Modules, Contributions to Algebra and geometry, 2004,        45 (1), 61-74.
4. G.Desale, W.K Nicholson, Endoprimitive rings, J. Algebra, 1981, 70, 548-560.
5. F. Kasch, Modules and Rings, Acad. Press, London, 1982.
6. A.G. Naoum, Flat modules and multiplication modules, Periodica Mathematica Hungarica 1990, 21,309-317.
7. A.G Naoum, V2 Cancellation modules, Kyungpook Mathematical Journal 1996, 36, 97-106.
8. M.S. Abbas, On fully stable modules, Ph.D. Thesis, University of Baghdad 1991.
9. D.J. Fieldhouse, Pure simple and indecomposable rings, Can. Math Bull. 1970, 13, 71-78.
10. N.V. Dung, D.V. Huynh, P.F Smith and R. Wisbauer, Extending Modules, Pitman Research Notes in Mathematic Series 313,             Longman, New York, 1994.
11. A.G. Naoum and S.M Yaseen. The regular submodules of a module, commentations in mathematica XXXV, 1995, 195-201.
12. A.G Naoum and B.H. Al-Bahraany, Modules with the pure sum propery, submitted. 
13. B.H. Al-Bahraany, Modules with the pure intersection property, Ph.D. Thesis, University of Baghdad, 2000.