Weakly continuous modules
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CitationShirinkam, S., Ghalandarzadeh, SH. ve Malakooti Rad, P. (2009). Weakly continuous modules. Maltepe Üniversitesi. s. 355.
Let 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.
SourceInternational Conference of Mathematical Sciences
- Makale Koleksiyonu 
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