Resolution and tor algebra structures of grade 3 ideals defining compressed rings

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.

Separative Ideals of Exchange Rings

On $z$-ideals of pointfree function rings

Let $L$ be a completely regular frame and $mathcal{R}L$ be the ‎ring of continuous real-valued functions on $L$‎. ‎We show that the‎ ‎lattice $Zid(mathcal{R}L)$ of $z$-ideals of $mathcal{R}L$ is a‎ ‎normal coherent Yosida frame‎, ‎which extends the corresponding $C(X)$‎ ‎result of Mart'{i}nez and Zenk‎. ‎This we do by exhibiting‎ ‎$Zid(mathcal{R}L)$ as a quotient of $Rad(mathcal{R}L)$‎, ‎the‎ ‎...

Picard-graded Betti Numbers and the Defining Ideals of Cox Rings

Different choices of basis yield (non-canonically) isomorphic Cox rings and any of them is a “total” coordinate ring for X in the sense that, (1) The homogeneous coordinate rings ⊕∞ s=0H (X, sD) of all images of X via complete linear systems φD : X → P(H(X,D)) are subalgebras of Cox(X). (2) If the Cox ring is a finitely generated k-algebra then X can be obtained as a quotient of an open set of ...

Fuzzy Group Ideals and Rings

This section define a level subring or level ideals obtain a set of necessary and sufficient condition for the equality of two ideals and characterizes field in terms of its fuzzy ideals. It also presents a procedure to construct a fuzzy subrings (fuzzy ideals) from any given ascending chain of subring ideal. We prove that the lattice of fuzzy congruence of group G (respectively ring R) is isom...