In this paper, we introduce and study the notion of HB-closed sets in L-topological space. Then, HB-convergence theory for L-molecular nets and L-ideals is established in terms of HB-closedness. Finally, we give a new...In this paper, we introduce and study the notion of HB-closed sets in L-topological space. Then, HB-convergence theory for L-molecular nets and L-ideals is established in terms of HB-closedness. Finally, we give a new definition of fuzzy H-continuous [1] which is called HB-continuity on the basis of the notion of H-bounded L-subsets in L-topological space. Then we give characterizations and properties by making use of HB-converges theory of L-molecular nets and L-ideals.展开更多
Let R be a prime ring and m, n be fixed non-negative integers such that m＋n ≠ 0. Suppose L is an （m＋m＋1）-power closed Lie ideal, and this means ure＋n＋1 ∈ L for all u ∈ L. If charR = 0 or a prime p 〉 2（m ...Let R be a prime ring and m, n be fixed non-negative integers such that m＋n ≠ 0. Suppose L is an （m＋m＋1）-power closed Lie ideal, and this means ure＋n＋1 ∈ L for all u ∈ L. If charR = 0 or a prime p 〉 2（m ＋ n）, we characterize the additive maps d： L → R satisfying d（um＋n＋1） = （m -＋n ＋ 1）umd（u）un （resp., d（um＋n＋l） = umd（u）un） for all u ∈ L.展开更多
Herzog,Hibi,Hreinddttir et al.introduced the class of closed graphs,and they proved that the binomial edge ideal JG of a graph G has quadratic GrSbner bases if G is closed.In this paper,we introduce the class of weakl...Herzog,Hibi,Hreinddttir et al.introduced the class of closed graphs,and they proved that the binomial edge ideal JG of a graph G has quadratic GrSbner bases if G is closed.In this paper,we introduce the class of weakly closed graphs as a generalization of the closed graph,and we prove that the quotient ring S/JG of the polynomial ring S=K[x1,...,xn,y1,...,yn]with K a field and n=|V(G)|is F-pure if G is weakly closed.This fact is a generalization of Ohtani's theorem.展开更多
文摘In this paper, we introduce and study the notion of HB-closed sets in L-topological space. Then, HB-convergence theory for L-molecular nets and L-ideals is established in terms of HB-closedness. Finally, we give a new definition of fuzzy H-continuous [1] which is called HB-continuity on the basis of the notion of H-bounded L-subsets in L-topological space. Then we give characterizations and properties by making use of HB-converges theory of L-molecular nets and L-ideals.
文摘Let R be a prime ring and m, n be fixed non-negative integers such that m＋n ≠ 0. Suppose L is an （m＋m＋1）-power closed Lie ideal, and this means ure＋n＋1 ∈ L for all u ∈ L. If charR = 0 or a prime p 〉 2（m ＋ n）, we characterize the additive maps d： L → R satisfying d（um＋n＋1） = （m -＋n ＋ 1）umd（u）un （resp., d（um＋n＋l） = umd（u）un） for all u ∈ L.
文摘Herzog,Hibi,Hreinddttir et al.introduced the class of closed graphs,and they proved that the binomial edge ideal JG of a graph G has quadratic GrSbner bases if G is closed.In this paper,we introduce the class of weakly closed graphs as a generalization of the closed graph,and we prove that the quotient ring S/JG of the polynomial ring S=K[x1,...,xn,y1,...,yn]with K a field and n=|V(G)|is F-pure if G is weakly closed.This fact is a generalization of Ohtani's theorem.
