In this paper we investigate the class of rigid monomial ideals. We give a characterization of the minimal free resolutions of certain classes of these ideals. Specifically, we show that the ideals in a particular subclass of rigid monomial ideals are lattice-linear and thus their minimal resolution can be constructed as a poset resolution. We then use this result to give a description of the m...

Lattice games are real-valued functions de...ned on a ...nite lattice L. The basic players are the nonzero join-irreducible elements of the lattice and the coalitions are its elements. If L is the Boolean algebra 2 then we obtain a n-person game. Gilboa and Lehrer introduced the global games, which are lattice games where L = ¦n, the lattice of all partitions of N ordered by re...nement. Faigle...

To each closed subset S of a finite dimensional Euclidean space corresponds a σ-ideal of sets J (S) which is σ-generated over S by the convex subsets of S. The set-theoretic properties of this ideal hold geometric information about the set. We discuss the relation of reducibility between convexity ideals and the connections between convexity ideals to other types of ideals, such as the ideals w...

Let $L$ be a completely regular frame and $mathcal{R}L$ be the ring of continuous real-valued functions on $L$. We study the frame $mathfrak{O}(Min(mathcal{R}L))$ of minimal prime ideals of $mathcal{R}L$ in relation to $beta L$. For $Iinbeta L$, denote by $textit{textbf{O}}^I$ the ideal ${alphainmathcal{R}Lmidcozalphain I}$ of $mathcal{R}L$. We show that sending $I$ to the set of minimal prime ...

A right ideal (left ideal, two-sided ideal) is a non-empty language L over an alphabet Σ such that L = LΣ∗ (L = Σ∗L, L = Σ∗LΣ∗). Let k = 3 for right ideals, 4 for left ideals and 5 for two-sided ideals. We show that there exist sequences (Ln | n > k) of right, left, and two-sided regular ideals, where Ln has quotient complexity (state complexity) n, such that Ln is most complex in its class und...

The intersection of all two-sided ideals of an ordered semigroup, if it is non-empty, is called the kernel of the ordered semigroup. A left ideal L of an ordered semigroup (S, ·,≤) having a kernel I is said to be simple if I is properly contained in L and for any left ideal L′ of (S, ·,≤), I is properly contained in L′ and L′ is contained in L imply L′ = L. The notions of simple right and two-s...

let $l$ be a completely regular frame and $mathcal{r}l$ be the ringof continuous real-valued functions on $l$. we study the frame$mathfrak{o}(min(mathcal{r}l))$ of minimal prime ideals of$mathcal{r}l$ in relation to $beta l$. for $iinbeta l$, denoteby $textit{textbf{o}}^i$ the ideal${alphainmathcal{r}lmidcozalphain i}$ of $mathcal{r}l$. weshow that sending $i$ to the set of minimal prime ideals...

In the paper, we give the concept of ¬-ideals dual to that of ¬-filters by using the operation ~ in SBL¬-algebras, and also show some characterizations of ¬-ideals. The relationships between ¬-ideals and ¬filter are investigated by the notion of the set of complement elements. It is obtained that for a ¬-proper ideal I of a SBL¬-algebra L, the set I ∪N(I) is the least SBL¬-subalgebra of L conta...