We investigate how the chain property for the associated primes of monomial degenerations of toric (or lattice) ideals can be generalized to arbitrary A-graded ideals. The generalization works in dimension d = 2, but it fails for d ≥ 3.

The correspondence between unmixed bipartite graphs and sublattices of the Boolean lattice is discussed. By using this correspondence, we show the existence of squarefree quadratic initial ideals of toric ideals arising from minimal vertex covers of unmixed bipartite graphs.

The concept of  -ideals is introduced in an Almost Distributive lattice(ADL) with respect to a congruence and the properties of  -ideals are studied. Derived a set of equivalent conditions for a  -ideal to become a  -prime ideal.

We compute the initial ideals, with respect to certain conveniently chosen term orders, of ideals of tangent cones at torus fixed points to Schubert varieties in orthogonal Grassmannians. The initial ideals turn out to be square-free monomial ideals and therefore StanleyReisner face rings of simplicial complexes. We describe these complexes. The maximal faces of these complexes encode certain s...

Achieving the goals in the title (and others) relies on a cardinality-wise scanning of the ideals of the poset. Specifically, the relevant numbers attached to the k + 1 elment ideals are inferred from the corresponding numbers of the k-element (order) ideals. Crucial in all of this is a compressed representation (using wildcards) of the ideal lattice. The whole scheme invites distributed comput...

Let L be a complete lattice. In this paper we introduce various definitions of L-fuzzy 2-absorbing ideals of a commutative ring R and give some basic results concerning these classes of ideals.

In this paper various properties of the spectrum (i.e. the set of prime elements endowed with the hull-kernel topology) of a distributive continuous lattice are developed. It is shown that the spectrum is always a locally quasicompact sober space and conversely that the lattice of open sets of a locally quasicompact sober space is a continuous lattice. Algebraic lattices are a special subclass ...

In this paper, we apply the concept of fuzzy soft sets to ordered semigroup theory. The concepts of (∈γ ,∈γ ∨qδ)-fuzzy left (right) ideals, (∈γ ,∈γ ∨qδ)-fuzzy biideals and (∈γ ,∈γ ∨qδ)-fuzzy quasi-ideals are introduced and some related properties are obtained. Three kinds of lattice structures of the set of all (∈γ ,∈γ ∨qδ)-fuzzy soft left (right) ideals of an ordered semigroup are derived. The...

This paper is to study the rough sets within the context of lattices. We study the special properties of the rough sets which can be constructed by means of the congruences determined by ideals of lattice. Also the properties of the generalized rough sets with respect to ideals of lattice are investigated. Finally we give an example of their application in formal concept analysis. 2014 Elsevier...

In this paper we primarily study monomial ideals and their minimal free resolutions by studying their associated lcm-lattices. In particular, we formally define the notion of coordinatizing a finite atomic lattice P to produce a monomial ideal whose lcm-lattice is P , and we give a characterization of all such coordinatizations. We prove that all relations in the lattice L(n) of all finite atom...