On 2-absorbing ideals of MV-algebras

Abstract

In this paper, we introduce the concept of 2-absorbing ideals in MV-algebras which is a generalization of prime ideals. A number of results concerning 2-absorbing ideals and examples of these ideals are given and some of their properties are investigated. Intersection of two prime ideals is not necessarily a prime ideal, we prove that this intersection is a 2-absorbing ideal. Also, we investigate number of minimal prime ideals on 2-absorbing ideal in dierent situations. Moreover, if every 2-absorbing ideal is a maximal ideal in an MV-algebra, then that MV-algebra has at most one prime ideal. Finally, it is shown that every ideal can be expressed as an intersection of 2-absorbing ideals that contain it.