Shirinkam, S.Ghalandarzadeh, SH.Malakooti Rad, P.2024-07-122024-07-122009Shirinkam, S., Ghalandarzadeh, SH. ve Malakooti Rad, P. (2009). Weakly continuous modules. Maltepe Üniversitesi. s. 355.9.78605E+12https://hdl.handle.net/20.500.12415/2493Let R be a commutative ring with identity and M be an unitary R-module. In this article we investigate the concept of weakly continuous modules as a natural generalization of weakly continuous rings. M is called weakly continuous if the annihilator of each element of M is essential in a summand of R, and M satisfies the C2-condition. Also M is called F -semiregular if for every x ? M, there exists a decomposition M = A ? B such that A is projective, A ? Rx and Rx ? B ? F . If M is a module, the following conditions are equivalent for m ? M: (1) Ann(m) ?ess eR for some e 2 = e ? R.(2) mR = P ? S where P is projective and S is singular submodule. M is called ACS module if the above conditions are satisfied for every element m ? M. We investigate some equivalent conditions of weakly continuous multiplication modules. An R-module M is a multiplication module if for every submodule K of M there is an ideal I of R such that K = IM. A submodule N of M is idempotent if (N : M)N = N. Let the following statements.enCC0 1.0 Universalinfo:eu-repo/semantics/openAccessConference Object356355