Abstract
In this paper, we introduce and investigate essentially M-slightly compressible modules and essentially M-slightly compressible injective modules. It has been shown that over hereditary ring R and M is an injective right R-module. If N is an essentially M-slightly compressible module then every essential submodule A of N containing a direct summand of N. For any ring R and uniform right R-module M, we can show that N is an essentially M-slightly compressible injective module if and only if N is an M-slightly compressible injective module.
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