in this paper, we construct two fuzzy sets using the notions of level subsets and strong level subsets of a given fuzzy set in a ring r. these fuzzy sets turn out to be identical and provide a universal construction of a fuzzy ideal generated by a given fuzzy set in a ring. using this construction and employing the technique of strong level subsets, we provide the shortest and direct fuzzy set ...

The main purpose of this paper is to continue the study of uniform strong primeness on fuzzy setting. A pure fuzzy notion of this structure allows us to develop specific fuzzy results on USP (uniformly strongly prime) ideals over commutative and noncommutative rings. Besides, the differences between crisp and fuzzy setting are investigated. For instance, in crisp setting an ideal I of a ring R ...

Due to the elimination property held by the lexicographic monomial order, the corresponding Gröbner bases display strong structural properties from which meaningful informations can easily be extracted. We study these properties for radical ideals of (co)dimension zero. The proof presented relies on a combinatorial decomposition of the finite set of points whereby iterated Lagrange interpolatio...

We relate the (co)homological properties of real coordinate subspace arrangements and of monomial ideals.

We prove the multiplicity bounds conjectured by Herzog-HunekeSrinivasan and Herzog-Srinivasan in the following cases: the strong conjecture for edge ideals of forests, and the weaker Taylor bound conjecture for all quadratic monomial ideals. We determine when equality holds in the conjectured bound, and verify that when equality holds, the resolution is pure. We characterize forests that have C...

The problem of efficient implementation of two-dimensional interpolation in the Guruswami-Sudan list decoding algorithm for Reed-Solomon codes is considered. It is shown that it can be implemented by computing the product of the ideals of interpolation polynomials constructed for subsets of interpolation points. A method for fast multiplication of zero-dimensional co-prime ideals product is pro...