TY - JOUR ID - 202 TI - Applications of epi-retractable modules JO - Bulletin of the Iranian Mathematical Society JA - BIMS LA - en SN - 1017-060X AU - Pandeya, Bashishth Muni AU - Chaturvedi, Avanish Kumar AU - Gupta, Ashok Ji AD - Department of Applied Mathematics, Institute of Technology, Banaras Hindu University, Varanasi-221005, India. AD - Department of Mathematics, Jaypee Institute of Information Technology, (Deemed University) A-10, Sector-62, Noida-201307 (UP), India Y1 - 2012 PY - 2012 VL - 38 IS - 2 SP - 469 EP - 477 KW - Epi-retractable modules KW - semi-simple rings KW - Perfect rings KW - Hereditary rings KW - von-Numann regular rings DO - N2 - 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. UR - http://bims.iranjournals.ir/article_202.html L1 - http://bims.iranjournals.ir/article_202_388757ddee7a3a67ab050c9a998e2049.pdf ER -