In this paper, we introduce and study small-semiessential subsemimodules as extension of semiessential subsemimodules. We show a characterization of small-semiessential subsemimodules in which the radical allows to establish a correspondence with semiessential subsemimodules. Then, with this procedure, we extended some well known results in semiessential subsemimodules to small-semiessential subsemimodules.

small-semiessential subsemimodule, superfluous subsemimodule, semiessential subsemimodule, radical of a semimodule.