‎in this article we introduce $mu$-filtered fuzzy module with a family of fuzzy submodules.  it shows the relation between $mu$-filtered fuzzy modules and crisp filtered modules by level sets. we investigate fuzzy topology on the $mu$-filtered fuzzy module and apply that to introduce fuzzy completion. finally we extend krull's intersection theorem of fuzzy ideals by using concept $mu$-adic...

in this paper‎, ‎we give a complete proof of theorem 4.1(ii) and a new‎ ‎elementary proof of theorem 4.1(i) in [li and shen‎, ‎on the‎ ‎intersection of the normalizers of the derived subgroups of all‎ ‎subgroups of a finite group‎, ‎ j‎. ‎algebra, ‎323  (2010) 1349--1357]‎. ‎in addition‎, ‎we also give a generalization of baer's theorem‎.

This paper focuses on the relationship between an $L$-subset and the system of level-elements induced by it, where the underlying lattice $L$ is a complete residuated lattice and the domain set of $L$-subset is an $L$-partially ordered set $(X,P)$. Firstly, we obtain the sufficient and necessary condition that an $L$-subset is represented by its system of level-elements. Then, a new representat...

In this paper,we deeply research Lagrange interpolation of n-variables and give an application of Cayley-Bacharach theorem for it. We pose the concept of sufficient intersection about s(1 ≤ s ≤ n) algebraic hypersurfaces in n-dimensional complex Euclidean space and discuss the Lagrange interpolation along the algebraic manifold of sufficient intersection. By means of some theorems ( such as Bez...

In this paper‎, ‎we give a complete proof of Theorem 4.1(ii) and a new‎ ‎elementary proof of Theorem 4.1(i) in [Li and Shen‎, ‎On the‎ ‎intersection of the normalizers of the derived subgroups of all‎ ‎subgroups of a finite group‎, ‎ J‎. ‎Algebra, ‎323  (2010) 1349--1357]‎. ‎In addition‎, ‎we also give a generalization of Baer's Theorem‎.

obtain a new for the of a-(u, A) design the block intersection designs are eliminated by an ad hoc coding theoretic argument. A 2-(v, k, A) design 93 is said to be quasi-symmetric if there are two block intersection sizes s1 and s2. The parameters of the complementary design !3* are related to the parameters of 93 as follows: Here Ai denotes the number of blocks through a given i points (and A ...

Helly’s theorem is one of the fundamental results in discrete geometry [9]. It states that if every 6 d+1 sets in a set system S of convex sets in R have non-empty intersection then all of the sets in S have non-empty intersection. Equivalently, if the entire family S has empty intersection, then there is a subset S ′ ⊂ S (a witness) of size 6 d+1 which also has empty intersection. Over the yea...

The well-known Erdős–Ko–Rado Theorem states that if F is a family of k-element subsets of {1, 2, . . . , n} (n ≥ 2k) satisfying S, T ∈ F ⇒ |S ∩ T | ≥ 1, then |F| ≤ ( n−1 k−1 ) . The theorem also provides necessary and sufficient conditions for attaining the maximum. We present elementary methods for deriving generalizations of the Erdős– Ko–Rado Theorem on several classes of combinatorial objec...