It is well known that the set of all ideals(2) of a ring forms a complete modular lattice with respect to set inclusion. The same is true of the set of all right ideals. Our purpose in this paper is to consider the consequences of imposing certain additional restrictions on these ideal lattices. In particular, we discuss the case in which one or both of these lattices is complemented, and the c...

In this paper, we intend to study a connection between rough sets and lattice theory. We introduce the concepts of upper and lower rough ideals (filters) in a lattice. Then, we offer some of their properties with regard to prime ideals (filters), the set of all fixed points, compact elements, and homomorphisms. 2012 Elsevier Inc. All rights reserved.

In this paper we completely characterize lattice ideals that are complete intersections or equivalently complete intersections finitely generated semigroups of ZZn ⊕ T with no invertible elements, where T is a finite abelian group. We also characterize the lattice ideals that are set-theoretic complete intersections on binomials.

We introduce a monomial ideal whose standard monomials encode the vertices of all fibers of a lattice. We study the minimal generators, the radical, the associated primes and the primary decomposition of this ideal, as well as its relation to initial ideals of lattice ideals.

In this paper we investigate further properties of fuzzy ideals of a BL-algebra. The notions of fuzzy prime ideals, fuzzy irreducible ideals, and fuzzy Gödel ideals of a BL-algebra are introduced and their several properties are investigated. We give a procedure to generate a fuzzy ideal by a fuzzy set. We prove that every fuzzy irreducible ideal is a fuzzy prime ideal but a fuzzy prime ideal m...

In this paper authors have given a separation theorem for α ideals in a 0distributive lattice. Some characterizations of semi prime ideals have been discussed. Then they have included an interesting result on *-ideals in a p-algebra by using the properties of semi prime ideals.

A family of 2א0 Borel ideals on a compact lattice are constructed such that no two quotient lattices by ideals from this family are isomorphic.

We characterize a fuzzy lattice through a fuzzy partial order relation, define ideals and filters of fuzzy lattices, characterize an ideal of fuzzy lattice using its level set and its support and show that a subset of a fuzzy lattice is an ideal if and only if its support is an ideal. Similarly, we show the same for its level set. Lastly, we define some kinds of ideals and filters of fuzzy latt...

Our aim in this paper is to introduce and study a new sort of fuzzy sublattice (ideal, filter) of a lattice called ) q , ( ∨ ∈ ∈ -fuzzy sublattice (ideal, filter). These fuzzy sublattices (ideals, filters) are characterized by their level sublattices (ideals, filters). Finally, we give a generalization of ) q , ( ∨ ∈ ∈ -fuzzy sublattices (ideals, filters).

y Abstract This paper presents a framework for comparing two strictness analysis techniques: Abstract interpretation and non{standard type inference. The comparison is based on the representation of a lattice by its ideals. A formal system for deducing inclusions between ideals of a lattice is presented and proved sound and complete. Viewing the ideals as strictness properties we use the formal...