The major results of Robertson and Seymour on graph well-quasi-ordering establish nonconstructively that many natural graph properties that constitute ideals in the minor or immersion orders are characterized by a nite set of forbidden sub-structures termed the obstructions for the property. This raises the question of what general kinds of information about an ideal are suucient, or insuucient...

The concept of quasi-coincidence of an interval-valued fuzzy set is considered. By using this new idea, the notion of interval-valued (α, β)−fuzzy k−ideals of semirings is introduced, which is a generalization of a fuzzy k−ideal. Also some related properties are studied and in particular, the interval-valued (∈,∈ ∨q)−fuzzy k−ideals in a semiring will be investigated. Finally, the concept of imp...

Nakayama (Ann. of Math. 42, 1941) showed that over an artinian serial ring every module is a direct sum of uniserial modules. Hence artinian serial rings have the property that each right (left) ideal is a finite direct sum of quasi-injective right (left) ideals. A ring with the property that each right (left) ideal is a finite direct sum of quasi-injective right (left) ideals will be called a ...

Let H d (t ≥ −d, t > −3) be the reproducing kernel Hilbert space on the unit ball B d with kernel k(z, w) = 1 (1− 〈z, w〉)d+t+1 . We prove that if an ideal I ⊳ C [z1 , . . . , zd] (not necessarily homogeneous) has what we call the approximate stable division property, then the closure of I in H d is p-essentially normal for all p > d. We then show that all quasi homogeneous ideals in two variabl...

We prove that each ideal of a locally formally equidimensional analytically un-ramiied Noetherian integral domain is the contraction of an ideal of a one-dimensional semilo-cal birational extension domain. We give an application to a problem concerning the primary decomposition of powers of ideals in Noetherian rings. It is shown in S2] that for each ideal I in a Noetherian commutative ring R t...

In this paper we describe the method which applied to successfully compute primary decomposition of a certain ideal coming from applications in combinatorial algebra and algebraic statistics regarding conditional independence statements with hidden variables. While our is based on algorithm for by Gianni, Trager Zacharias, were not able decompose using standard form that algorithm, nor any othe...