On G-algebra semi-group

In this work, we introduce the algebraic structure of semigroup with G-algebra is called GS-Algebra as extension of algebras QS-algebra and BP-algebra and then some basic properties are investigated. Several examples are presented. Also, some ideals in this concept are studied such as GS-ideal and closed-ideal. Some properties and characterizations of GS-ideal are presented. The relationships between GS-ideal and closed-ideal are studied. Furthermore, some results of GS-ideal in GS-Algebra under homomorphism are discussed. Finally, the graph (by its annihilator-ideal) as the simple graph with elements of a GS-Algebra is studied and some related properties are given. Several examples are presented and some theorems are proved.