En-semi prime subacts over monoids with zero

Abstract

Let S be a monoids with zero and A_s be a right S-act.  In this paper, we introduce the notion of En-semi prime subact of an S-act A_s which is defined as: A proper subact B of an S-act A_s is said to be En-semi prime subact, if whenever f²(a)S ⊆ B for some endomorphism f of an S-act A_s, and a ∈ A_s, then f(a)S ⊆ B.  An S-act A_s itself is called En-semi prime if the zero subact (θ) of A_s is En-semi prime subact of A_s.  Also, we study and give some related concepts of this notion like: semi prime subact, En-prime subact, En-pure subact and En-radical of subact.