Date Log
Submitted
Aug 6, 2020
Published
Mar 28, 2017
MODULES INVARIANT UNDER IDEMPOTENT HOMOMORPHISMS
Corresponding Author(s) : Truong Cong Quynh
tcquynh@ued.udn.vn
UED Journal of Social Sciences, Humanities and Education,
Vol. 7 No. 1 (2017): UED JOURNAL OF SOCIAL SCIENCES, HUMANITIES AND EDUCATION
Abstract
Let M be a right R-module. A quasi-injective module is characterized as follows: a module M is quasi-injective if and only if for any endomorphism f of the injective hull of the module M. Moreover, recently, automorphism-invariant modules (M is said to be automorphism-invariant if for any automorphism f of the injective hull of M) have been a research focus for many authors. In this article, we present some properties of module M of which every submodule N is invariant via idempotent elements of End(M).
Keywords
module; invaraint; idempotent; projection-invariant; injective
Phan The Hai, Truong Cong Quynh, & Le Thi Thanh. (2017). MODULES INVARIANT UNDER IDEMPOTENT HOMOMORPHISMS. UED Journal of Social Sciences, Humanities and Education, 7(1), 9-15. https://doi.org/10.47393/jshe.v7i1.740
Download Citation
Endnote/Zotero/Mendeley (RIS)BibTeX
References
-
Camillo, V. P., Khurana. D., Lam, T. Y., Nicholson, W. K. and Zhou, Y. (2006), Continuous modules are clean, J. Al gebra, 304(1), pp.94-111.
[2] Fuchs, L. (1970), Infinite Abelian Groups, vol. I, Pure Appl. Math., Ser. Monogr. Textb., vol. 36, Academic Press, New York, San Francisco, London.
[3] Jeremy, L., (1974), Modules et anneaux quasi-continus, Can. Math. Bull. 17, pp.217-228.
[4] Johnson, R. E. and Wong, E. T., (1961), Quasi-injective modules and irreducible rings, J. London Math. Soc. 36, pp.260-268.
[5] Lee, T.K., and Zhou. Y., (2013), Modules which are invariant under automorphisms of their injective hulls, J. Algebra Appl, 12, (2).
[6] Nicholson, W.K., Yousif, M. F. (2003), Quasi-Frobenius Rings. Cambridge Univ. Press.
[7] Tercan, A., Yucel. A., (2016), Module Theory, Extending Modules and Generalizations. Published by Birkhauser Verlag AG, Switzerland.