On 2-absorbing ideals of MV-algebras

The concept of 2-absorbing ideals in MV-algebras, which generalizes the notion of prime ideals, is introduced in this paper. We present several results related to 2-absorbing ideals, provide examples, and explore some of properties. One notable result is that the intersection of two prime ideals, which is not necessarily a prime ideal, is shown to be a 2-absorbing ideal. The number of minimal prime ideals contained in a 2-absorbing ideal under different conditions are computed. Furthermore, we demonstrate that if every 2-absorbing ideal is maximal, then the MV-algebra can have at most one prime ideal. Finally, these new ideals are used to classify the ideals of MV-algebra.