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کاربرد نوع شرط:
- جایگاه : پژوهشی
- مجله: International Journal of Industrial Mathematics
- نوع مقاله: Journal Article
- کلمات کلیدی: ultra ideal,ideal,$MV$-algebra,Chines reminder theorem,Pseudo-hoops
- چکیده:
- چکیده انگلیسی: 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.
- انتشار مقاله: 23-10-1395
- نویسندگان: S. Saidi Goraghani,R. A. Borzooei
- مشاهده
- جایگاه : پژوهشی
- مجله: International Journal of Industrial Mathematics
- نوع مقاله: Journal Article
- کلمات کلیدی: Filter,Pseudo-hoop algebra,n-fold obstinate pseudo-hoop,n-fold obstinate filter
- چکیده:
- چکیده انگلیسی: In this paper, we introduce the concepts of n-fold obstinate pseudo-hoop and n-fold obstinate filter in pseudo-hoops. Then we investigated these notions and proved some properties of them. Also, we discussed the relationship between n-fold obstinate pseudo-hoop and n-fold obstinate filter and other types of n-fold pseudo-hoops and n-fold filters such as n-fold(positive) implicative filter and n-fold fantastic filter in pseudo-hoops. For example, we proved that any $n$-fold obstinate filter is a maximal filter. Finally, we obtain a characterization of n-fold obstinate filters in terms of congruences and we show that any n-fold obstinate pseudo-hoop is an n-fold fantastic, n-fold positive implicative, n-fold implicative pseudo-hoop and simple pseudo-hoop.
- انتشار مقاله: 17-07-1396
- نویسندگان: R. A. Borzooei,A. Namdar,M. Aaly Kologani
- مشاهده
- جایگاه : پژوهشی
- مجله: International Journal of Industrial Mathematics
- نوع مقاله: Journal Article
- کلمات کلیدی: Filter,Topological residuated lattice,Regular space,Normal space,(locally) Compact space.
- چکیده:
- چکیده انگلیسی: In this paper, we study the separtion axioms $T_0,T_1,T_2$ and $T_{5/2}$ on topological and semitopological residuated lattices and we show that they are equivalent on topological residuated lattices. Then we prove that for every infinite cardinal number $alpha$, there exists at least one nontrivial Hausdorff topological residuated lattice of cardinality $alpha$. In the follows, we obtain some conditions on (semi) topological residuated lattices under which this spaces will convert into regular and normal spaces. Finally by using of regularity and normality, we convert (semi)topological residuated lattices into metrizable topological residuated lattices.
- انتشار مقاله: 18-03-1396
- نویسندگان: N. Kouhestani,R. A. Borzooei
- مشاهده
- جایگاه : پژوهشی
- مجله: Algebraic Structures and Their Applications
- نوع مقاله: Journal Article
- کلمات کلیدی: $BCK$-algebra,(associative,commutative,positive implicative,implicative) ideal,ultra ideal,involution ideal
- چکیده:
- چکیده انگلیسی: In this paper, we define the notions of ultra and involution ideals in $BCK$-algebras. Then we get the relation among them and other ideals as (positive) implicative, associative, commutative and prime ideals. Specially, we show that in a bounded implicative $BCK$-algebra, any involution ideal is a positive implicative ideal and in a bounded positive implicative lower $BCK$-semilattice, the notions of prime ideals and ultra ideals are coincide.
- انتشار مقاله: 03-05-1395
- نویسندگان: Simin Saidi Goraghani,R. A. Borzooei
- مشاهده