Abstract
In this paper, we introduce the notion of prime gamma subact and study some of its properties. Also, we define the concept of product gamma subacts of gamma act, particularly product gamma subacts of multiplication gamma act then we obtain some related results. Using our concept to introduce new mathematical system which is called the semigroup associative with multiplication gamma act and its basic properties are discussed. Also, by definition of product gamma subacts, we introduce the concept of gamma nilpotent. Finally, the concepts of (meet principal and weak meet principle ) gamma subact are introduced to study the product of multiplication gamma ideals of gamma semigroups. Relation among the multiplication, meet principal and weak meet principle gamma subacts are investigated.
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