Let R be a Noetherian ring, F := Rr and M ⊆ F a submodule of rank r. Let A∗(M) denote the stable value of Ass(Fn/Mn), for n large, where Fn is the nth symmetric power of Fn and Mn is the image of the nth symmetric power of M in Fn. We provide a number of characterizations for a prime ideal to belong to A∗(M). We also show that A∗(M) ⊆ A∗(M), where A∗(M) denotes the stable value of Ass(Fn/Mn).

In this paper, the variational iteration method for solving nth-order fuzzy integro differential equations (nth-FIDE) is proposed. In fact the problem is changed to the system of ordinary fuzzy integro-differential equations and then fuzzy solution of nth-FIDE is obtained. Some examples show the efficiency of the proposed method.

Weyl’s theorem for an operator says that the complement in the spectrum of the Weyl spectrum coincides with the isolated points of the spectrum which are eigenvalues of finite multiplicity. H. Weyl ([22]) discovered that this property holds for hermitian operators and it has been extended from hermitian operators to hyponormal operators and to Toeplitz operators by L. Coburn ([5]), and to sever...

Let $(M^{2n},g)$ be a real hypersurface with recurrent shapeoperator and tangent to the structure vector field $xi$ of the Sasakian space form$widetilde{M}(c)$. We show that if the shape operator $A$ of $M$ isrecurrent then it is parallel. Moreover, we show that $M$is locally a product of two constant $phi-$sectional curvaturespaces.

This paper presents characterizations of M-fuzzifying matroids bymeans of two kinds of fuzzy operators, called M-fuzzifying derived operatorsand M-fuzzifying difference derived operators.