Generic lattice ideals

EMBEDDING OF THE LATTICE OF IDEALS OF A RING INTO ITS LATTICE OF FUZZY IDEALS

We show that the lattice of all ideals of a ring $R$ can be embedded in the lattice of all its fuzzyideals in uncountably many ways. For this purpose, we introduce the concept of the generalizedcharacteristic function $chi _{s}^{r} (A)$ of a subset $A$ of a ring $R$ forfixed $r , sin [0,1] $ and show that $A$ is an ideal of $R$ if, and only if, its generalizedcharacteristic function $chi _{s}^{...

Generic Gaussian ideals

The content of a polynomial f(t) is the ideal generated by its coefficients. Our aim here is to consider a beautiful formula of Dedekind–Mertens on the content of the product of two polynomials, to explain some of its features from the point of view of Cohen–Macaulay algebras and to apply it to obtain some Noether normalizations of certain toric rings. Furthermore, the structure of the primary ...

On lattice of basic z-ideals

  For an f-ring  with bounded inversion property, we show that   , the set of all basic z-ideals of , partially ordered by inclusion is a bounded distributive lattice. Also, whenever  is a semiprimitive ring, , the set of all basic -ideals of , partially ordered by inclusion is a bounded distributive lattice. Next, for an f-ring  with bounded inversion property, we prove that  is a complemented...

Generic Lattice

Reverse Lexicographic Initial Ideals of Generic Ideals Are Nitely Generated

This article generalizes the well-known notion of generic forms to the algebra R 0 , introduced in 27]. For the total degree, then reverse lexicographic order, we prove that the initial ideal of an ideal generated by nitely many generic forms (in countably innnitely many variables) is nitely generated. This contrasts to the lexicographic order, for which initial ideals of generic ideals in gene...