Let R be an arbitrary ring with identity and M a rightudR-module with S = EndR(M). In this paper, we introduce a class ofudmodules that is a generalization of principally projective (or simply p.p.)udrings and Baer modules. The module M is called endo-principally pro-udjective (or simply endo-p.p.) if for any m 2 M, lS(m) = Se for someude2 = e 2 S. For an endo-p.p. module M, we prove that M is endo-udrigid (resp., endo-reduced, endo-symmetric, endo-semicommutative) ifudand only if the endomorphism ring S is rigid (resp., reduced, symmetric,udsemicommutative), and we also prove that the module M is endo-rigid ifudand only if M is endo-reduced if and only if M is endo-symmetric if andudonly if M is endo-semicommutative if and only if M is abelian. Amongudothers we show that if M is abelian, then every direct summand of anudendo-p.p. module is also endo-p.p.udAMS Mathematics Subject Classi cation (2010): 13C99, 16D80, 16U80.udKey words and phrases: Baer modules, quasi-Baer modules, endo-princi-udpally quasi-Baer modules, endo-p.p. modules, endo-symmetric modules,udendo-reduced modules, endo-rigid modules, endo-semicommutative mod-udules, abelian modules.
展开▼
