Stanley–Reisner rings and the radicals of lattice ideals

Stanley-reisner Rings and the Radicals of Lattice Ideals

In this article we associate to every lattice ideal IL,ρ ⊂ K[x1, . . . , xm] a cone σ and a graph Gσ with vertices the minimal generators of the Stanley-Reisner ideal of σ. To every polynomial F we assign a subgraph Gσ(F ) of the graph Gσ. Every expression of the radical of IL,ρ, as a radical of an ideal generated by some polynomials F1, . . . , Fs gives a spanning subgraph of Gσ, the ∪ s i=1Gσ...

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}^{...

VAGUE RINGS AND VAGUE IDEALS

In this paper, various elementary properties of vague rings are obtained. Furthermore, the concepts of vague subring, vague ideal, vague prime ideal and vague maximal ideal are introduced, and the validity of some relevant classical results in these settings are investigated.

z-Ideals and zº-Ideals in the Factor Rings of C(X)

Separative Ideals of Exchange Rings