Modules whose partial endomorphisms have a δ-small kernels
DOI:
https://doi.org/10.22199/issn.0717-6279-2020-04-0059Keywords:
Small submodules, δ-small submodules, Monoform modules, δ-small monoform modules, Artinian principal ideal ringAbstract
Let R be a commutative ring and M a unital R-module. A submodule N is said to be δ-small, if whenever N + L = M with M/L is singular, we have L = M. M is called δ-small monoform if any of its partial endomorphism has δ-small kernel. In this paper, we introduce the concept of δ-small monoform modules as a generalization of monoform modules and give some of their properties, examples and characterizations.
References
M. S. Abbass, “On fully stable modules”, Ph. D. Thesis, University of Baghdad Iraq, 1990.
S. Asgari and A. Haghany, “Generalizations of t-extending modules relative to fully invariant submodules”, Journal of the Korean Mathematical Society, vol. 49, no. 3, pp. 503–514, May 2012, doi: 10.4134/JKMS.2012.49.3.503
M. Barry and P.C. Diop, “Some properties related to commutative weakly FGI-rings”, JP Journal of algebra, number theory and application, vol. 19, no. 2, pp. 141-153, Dec. 2010. [On line]. Available: https://bit.ly/2VOfw5W
E. Buyukasik and C. Lomp, “When δ-semiperfect rings are semiperfect”, Turkish journal of mathematics, vol. 34, pp. 317-324, 2010, doi: 10.3906/mat-0810-15
A. D. Diallo, P. C. Diop, and M. Barry, “On e-small monoform modules”, JP Journal of algebra, number theory and application, vol. 40, no. 3, pp. 305-320, Jun. 2018. [On line]. Available: https://bit.ly/31OQJlY
M. A. Inaam Hadi and K. H. Marhoon, “Small monoform modules”, Ibn AL- Haitham journal for pure and applied science, vol. 27, no. 2, pp. 229-240, Aug. 2014. [On line]. Available: https://bit.ly/3f7IIfK
S. M. Khury, “Nonsingular retractable modules and their endomorphism rings”, Bulletin of the Australian Mathematical Society, vol. 43, no. 1, pp. 63-71, Feb. 1991, doi: 10.1017/S000497270002877X
T. Y. Lam, Lectures on modules and rings, New York, NY: Springer, 1999, doi: 10.1007/978-1-4612-0525-8
A. Ç. Özcan and M. Alkan, “Semiperfect modules with respect to a preradica", Communications in algebra, vol. 34, no. 3, pp. 841–856, Feb. 2006, doi: 10.1080/00927870500441593
P. F. Smith, “Compressible and related modules”, in Algebra groups, rings, modules and homological algebra, P. Goeteres and O.M.G Jenda, Boca Raton, FL: Chapman & Hall/CRC, 2006, doi: 10.1201/9781420010763
R. Tribak, “Finitely generated δ-supplemented modules are amply δ-supplemented”, Bulletin of the Australian Mathematical Society, vol. 86, no. 2, pp. 430-439, Feb. 2012, doi: 10.1017/S0004972711003406
J. M. Zelmanowitz, “Representation of rings with faithful polyform modules”,
Communications in algebra, vol. 14, no. 6, pp. 1141-1169, 1986, doi: 10.1080/00927878608823357
Y. Q. Zhou, “Generalization of perfect, semiperfect and semiregular rings”, Algebra colloquium, vol. 7, pp. 305-318, Aug. 2000, doi: 10.1007/s10011-000-0305-9
Published
How to Cite
Issue
Section
Copyright (c) 2020 Papa Cheikhou Diop, Abdoul Djibril Diallo
This work is licensed under a Creative Commons Attribution 4.0 International License.
-
Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.
