In this paper, the first integral method will be applied to integrate the Davey–Stewartson’s equation. Using this method, a few exact solutions will be obtained using ideas from the theory of commutative algebra. Finally, soliton solution will also be obtained using the traveling wave hypothesis.
In this paper we introduce β * * relation on the lattice of submodules of a module M . We say that submodules X, Y of M are β * * equivalent, Xβ * * Y , if and only if. We show that the β * * relation is an equivalence relation. We also investigate some general properties of this relation. This relation is used to define and study classes of Goldie-Rad-supplemented and Rad-H-supplemented modules. We prove M = A ⊕ B is Goldie-Radsupplemented if and only if A and B are Goldie-Rad-supplemented.
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