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Received: 2006-09-08

Revision Accepted: 2006-12-07

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Journal of Zhejiang University SCIENCE A 2007 Vol.8 No.6 P.939-945

http://doi.org/10.1631/jzus.2007.A0939


On generalized extending modules


Author(s):  ZENG Qing-yi

Affiliation(s):  Department of Mathematics, Zhejiang University, Hangzhou 310027, China; more

Corresponding email(s):   zqy67@163.com

Key Words:  Generalized extending modules, Singular, Co-H-rings


ZENG Qing-yi. On generalized extending modules[J]. Journal of Zhejiang University Science A, 2007, 8(6): 939-945.

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Abstract: 
A module M is called generalized extending if for any submodule N of M, there is a direct summand K of M such that NK and K/N is singular. Any extending module and any singular module are generalized extending. Any homomorphic image of a generalized extending module is generalized extending. Any direct sum of a singular (uniform) module and a semi-simple module is generalized extending. A ring R is a right Co-H-ring if and only if all right R modules are generalized extending modules.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

[1] Anderson, F.W., Fuller, K.R., 1974. Rings and Categories of Modules. Springer Verlag, Berlin.

[2] Chatters, A.W., Hajarnavis, C.R., 1977. Rings in which every complement right ideal is a direct summand. Quart. J. Math. Oxford, 28:61-80.

[3] Chatters, A.W., Khuri, S.M., 1980. Endomorphism rings of modules over non-singular CS rings. J. London Math. Soc., s2-21(3):434-444.

[4] Dung, N.V., Huynh, D.V., Smith, P.F., Wisbauer, R., 1994. Extending Modules. Pitman, London.

[5] Faith, C., 1976. Algebra II: Ring Theory. Springer-Verlag Berlin Heidelberg, New York.

[6] Goodearl, K.R., 1976. Ring Theory. Marcel Dekker Inc., New York and Basel.

[7] Oshiro, K., 1984. Lifting modules, extending modules and their appliciations to QF-rings. Hokkaido Math. J., 13:310-338.

[8] Zeng, Q.Y., Shi, M.H., 2006. On closed weak supplemented modules. J. Zhejiang Univ. Sci. A, 7(2):210-215.

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