Author:
Khareeba Hayder Sh.,Alwan Ahmed H.
Abstract
In this work generalized supplemented semimodules are defined which generalize generalized supplemented modules. We investigate some properties of these semimodules. We show that the finite sum of GS-semimodules is GS-semimodule. We also define WGS-semimodules and proved that a semiring S is semilocal if and only if every finitely generated semimodule is a WGS-semimodule. Furthermore, we prove that if A be a semimodule as well as Rad(A)≪A. Then A is a WGS-semimodule if and only if A/Rad(A) is semisimple.
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