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Let X be a T -module, T is a commutative ring with identity and K be a proper submodule of X. In this paper we introduce the concepts of 2-visible submodules and fully 2-visible modules as a generalizations of visible submodules and fully visible modules resp., where K is said to be 2-visible whenever K=I2 K for every nonzero ideal I of T and AT -module X is called fully 2-visible if for any proper submodule of it is 2-visible.Study some of the properties of these concepts also discuss the relationship 2-visible submodules and fully 2-visible modules with 2-pure submoules and other related submodules and modules resp. are given

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In this paper, we presented a special type of submodule named W-visible submodule, which is weaker than the visible submodule, where a proper submodule W of a T-module X is said to be W-visible if W = IW for some non-zero proper ideal I of T. Also, we presented the concept of W-fully visible module, where a module X over a ring T is said to be W-fully visible if any proper submodule of X is W-visible submodule. This concept is considered weaker than the concept of fully visible module. In this study, we achieved numerous results and characteristics that belong to this concept