New Results on Ideals in $MV$-‎algebras‎

الموضوعات : مجله بین المللی ریاضیات صنعتی

S. Saidi Goraghani ¹ (Department of Mathematics, Farhangian University, Tehran, Iran.)
R. A. Borzooei ² (Department of Mathematics, Shahid Beheshti University, Tehran, Iran.)

تاريخ الإرسال : 14 الخميس , ربيع الثاني, 1438 تاريخ التأكيد : 16 الإثنين , ذو الحجة, 1439 تاريخ الإصدار : 08 الجمعة , رمضان, 1441

الکلمات المفتاحية: ‎P‎seudo-‎hoops‎, Ideal, Ultra ‎ideal, $MV$-algebra, Chines reminder theorem,

ملخص المقالة :

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.