Strongly 2-absorbing subacts over monoids with unique zero

Document Type : Original Article


Hakim Sabzevari University


In this article, we introduce (strongly) 2-absorbing ideals of monoids and generalize them to (strongly) 2-absorbing subacts of an act over monoids. Among some useful lemmas, we show that the radical ideal of a strongly 2-absorbing ideal is either a prime ideal or the intersection of two ideals which are only distinct prime ideals minimal over it. Also, we prove that for each strongly 2-absorbing ideal I of a monoid, there exists a strongly 2-absorbing S-act A such that Ann(A) = I and vice versa. Moreover, some of their basic properties are developed.


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