naa a22 4500 510782280 CHVBK 20180411083251.0 cr unu---uuuuu 180411e20131101xx s 000 0 eng 10.1007/s11856-013-0033-8 doi (NATIONALLICENCE)springer-10.1007/s11856-013-0033-8 Huang Zhaoyong Department of Mathematics, Nanjing University, 210093, Nanjing, Jiangsu Province, P. R. China aut Gorenstein injective and strongly cotorsion modules [Elektronische Daten] [Zhaoyong Huang] By investigating the properties of some special covers and envelopes of modules, we prove that if R is a Gorenstein ring with the injective envelope of R R flat, then a left R-module is Gorenstein injective if and only if it is strongly cotorsion, and a right R-module is Gorenstein flat if and only if it is strongly torsionfree. As a consequence, we get that for an Auslander-Gorenstein ring R, a left R-module is Gorenstein injective (resp. flat) if and only if it is strongly cotorsion (resp. torsionfree). Hebrew University Magnes Press, 2013 Israel Journal of Mathematics Springer US; http://www.springer-ny.com 198/1(2013-11-01), 215-228 0021-2172 198:1<215 2013 198 11856 https://doi.org/10.1007/s11856-013-0033-8 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11856-013-0033-8 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Huang Zhaoyong Department of Mathematics, Nanjing University, 210093, Nanjing, Jiangsu Province, P. R. China aut NATIONALLICENCE 773 0- Israel Journal of Mathematics Springer US; http://www.springer-ny.com 198/1(2013-11-01), 215-228 0021-2172 198:1<215 2013 198 11856 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer