New Results on Ideals in MV -algebras

In the present paper, by considering the notion of ideals in MV -algebras, we study some kinds of ideals in MV -algebras and obtain some results on them. For example, we present definition of ultra ideal in MV -algebras, and we get some results on it. In fact, by de nition of ultra ideals, we present new conditions to have prime ideals, positive implicative ideals and maximal ideals in MV -algebras. Also, we state some properties on contracted or extended ideals as useful examples of ideals in MV -algebras. Finally, we try to prove the Chines reminder theorem in MV -algebras.