ESSENTIALLY SLIGHTLY COMPRESSIBLE MODULES AND RINGS

Abstract

In this paper, the concepts of essentially slightly compressible modules and essentially slightly compressible rings are introduced, and related properties are investigated. The notion of essentially slightly compressible modules and rings are generalization of essentially compressible modules and rings introduced by [P. F. Smith and M. R. Vedadi, Essentially compressible modules and rings, J. Algebra304 (2006) 812–831]. I have also provided the characterization of such modules in terms of nonsingular injective modules. It has been shown that over a noetherian ring for a uniform module, essentially slightly compressible modules, slightly compressible modules and nonzero homomorphism from M into U for a nonzero uniform submodule U of M are equivalent. Throughout this paper, all rings are associative and all modules are unital right R-modules.