Abstract:We introduce the notion of an automorphism liftable module and give a characterization to it. We prove that category equivalence preserves automorphism liftable. Furthermore, we characterize semisimple rings, perfect rings, hereditary rings and quasi-Frobenius rings by properties of automorphism liftable modules. Also, we study automorphism liftable modules with summand sum property (SSP) and summand intersection property (SIP).
Keywords: dual automorphism invariant module; supplemented module; semisimple ring; perfect ring; summand sum property
DOI: DOI 10.14712/1213-7243.2015.237
AMS Subject Classification: 16L30 16D40 16W20