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 -