New Results on Ideals in $MV$-algebras
Subject Areas : International Journal of Industrial MathematicsS. Saidi Goraghani 1 , R. A. Borzooei 2
1 - Department of Mathematics, Farhangian University, Tehran, Iran.
2 - Department of Mathematics, Shahid Beheshti University, Tehran, Iran.
Keywords: Pseudo-hoops, Ideal, Ultra ideal, $MV$-algebra, Chines reminder theorem,
Abstract :
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 definition of ultra ideals, we present new conditions to have prime ideals, positive implicative ideals and maximal ideals in $MV$-algebras.