1
Department of Applied Mathematics, Institute of Technology, Banaras Hindu University, Varanasi-221005, India.
2
Department of Mathematics, Jaypee Institute of Information Technology, (Deemed University) A-10, Sector-62, Noida-201307 (UP), India
Abstract
An R-module M is called epi-retractable if every submodule of MR is a homomorphic image of M. It is shown that if R is a right perfect ring, then every projective slightly compressible module MR is epi-retractable. If R is a Noetherian ring, then every epi-retractable right R-module has direct sum of uniform submodules. If endomorphism ring of a module MR is von-Neumann regular, then M is semi-simple if and only if M is epi-retractable. If R is a quasi Frobenius ring, then R is a right hereditary ring if and only if every injective right R-module is semi-simple. A ring R is semi-simple if and only if R is right hereditary and every epiretractable right R-module is projective. Moreover, a ring R is semi-simple if and only if R is a pri and von-Neumann regular.
Pandeya, B. Muni, Chaturvedi, A. Kumar & Gupta, A. Ji. (2012). Applications of epi-retractable modules. Bulletin of the Iranian Mathematical Society, 38(2), 469-477.
MLA
Pandeya, B. Muni, Chaturvedi, A. Kumar, & Gupta, A. Ji. "Applications of epi-retractable modules", Bulletin of the Iranian Mathematical Society, 38, 2, 2012, 469-477.
HARVARD
Pandeya B. Muni, Chaturvedi A. Kumar, Gupta A. Ji. (2012). 'Applications of epi-retractable modules', Bulletin of the Iranian Mathematical Society, 38(2), pp. 469-477.
CHICAGO
B. Muni Pandeya, A. Kumar Chaturvedi & A. Ji Gupta, "Applications of epi-retractable modules," Bulletin of the Iranian Mathematical Society, 38 2 (2012): 469-477,
VANCOUVER
Pandeya B. Muni, Chaturvedi A. Kumar, Gupta A. Ji. Applications of epi-retractable modules. BIMS. 2012;38(2):469-477.
