Modules in which every surjective endomorphism has an e-small kernel
DOI:
https://doi.org/10.31642/JoKMC/2018/100118Keywords:
Hopfian module, generalized Hopfian module, e-small submodule , e-gH module.Abstract
In this paper we introduce the notion of e-gH modules which is a proper generalization of Hopfian modules and defined as, a module is called e-gH if, any surjective -endomorphism of has an e-small kernel, a ring is called e-gH if, is e-gH. We give some characterizations and properties of this modules.
Downloads
References
M.S. Abbas, On fully stable modules, Ph.D. Thesis, Univ. of Baghdad, Iraq, 1990.
Sh. Asgari and A. Haghany, T-extending modules and t-Baer modules, Comm. Algebra 39(2011), 1605-1623 DOI: https://doi.org/10.1080/00927871003677519
J. Clark, C. Lomp, N. Vanaja, and R. Wisbauer, Lifting modules, supplements and projectivity in module theory, Front. Math., Birkhäuser, Basel (2006).
F. Kasch, Modules and rings, 1982.
T.Y. Ghawi, Some generalizations of g-lifting modules, Quasigroups and Related Systems, 2022, to appear.
A. Ghorbani and A. Haghany, Generalized Hopfian modules, Journal of Algebra 255(2002), p. 324-341. DOI: https://doi.org/10.1016/S0021-8693(02)00124-2
K. R. Goodearl, Ring theory, Nonsingular rings and modules, Dekker, Newyork, 1976.
V. A. Hiremath, Hopfian rings and Hopfian modules, Indian J. Pure Appl. Math. 17 (1986), p. 895-900.F. Kasch, Modules and rings module, 1982.
K. Varadarajan, Hopfian and co-Hopfian objects, Publ. Mat. 36 (1992), p. 293-317. DOI: https://doi.org/10.5565/PUBLMAT_36192_21
D.X. Zhou, and X.R. Zhang, small-essential submodule and morita duality, south-east Asian Bull. Math. 35(2011) 1051-1062
Downloads
Published
How to Cite
Issue
Section
Categories
License
Copyright (c) 2023 osama mohammed
This work is licensed under a Creative Commons Attribution 4.0 International License.
which allows users to copy, create extracts, abstracts, and new works from the Article, alter and revise the Article, and make commercial use of the Article (including reuse and/or resale of the Article by commercial entities), provided the user gives appropriate credit (with a link to the formal publication through the relevant DOI), provides a link to the license, indicates if changes were made and the licensor is not represented as endorsing the use made of the work.
