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...

In the paper we present some auxiliary facts concerning posets and maps between them. Our main purpose, however is to give an account on complete lattices and lattices of ideals. A sufficient condition that a lattice might be complete, the fixed-point theorem and two remarks upon images of complete lattices in monotone maps, introduced in [10, pp. 8–9], can be found in Section 7. Section 8 deal...

In the paper we present some auxiliary facts concerning posets and maps between them. Our main purpose, however is to give an account on complete lattices and lattices of ideals. A sufficient condition that a lattice might be complete, the fixed-point theorem and two remarks upon images of complete lattices in monotone maps, introduced in [9, pp. 8–9], can be found in Section 7. Section 8 deals...

The study of semigroup algebras has a long tradition in commutative algebra. Presentation ideals of semigroup algebras are called toric ideals, in reference to their prominent role in geometry. In this paper we consider the more general class of lattice ideals. Fix a polynomial ring S = k[x1, . . . , xn] over a field k and identify monomials x in S with vectors a ∈ N. Let L be any sublattice of...

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...

In this paper we define a correspondence between the set of all fuzzy hideals of a Γ-hemiring S and the set of all fuzzy h-ideals of the operator hemirings of that Γ-hemiring. We deduce that the lattice of all fuzzy hideals of a Γ-hemiring is isomorphic to the lattice of all fuzzy h-ideals of the operator hemirings of that Γ-hemiring. Finally, the cartesian product of corresponding fuzzy h-idea...

From algebraic geometry perspective database relations are succinctly defined as Finite Varieties. After establishing basic framework, we give analytic proof of Heath’s theorem from Database Dependency theory. Next, we leverage Algebra-Geometry dictionary and focus on algebraic counterparts of finite varieties – [polynomial] Ideals. It is well known that intersection and sum of ideals are latti...

Squarefree monomial ideals arising from finite meet-semilattices and their free resolutions are studied. For the squarefree monomial ideals corresponding to poset ideals in a distributive lattice the Alexander dual is computed.

In the present paper, the intuitionistic fuzzy LI -ideal theory in lattice implication algebras is further studied. Some new properties and equivalent characterizations of intuitionistic fuzzy LI -ideals are given. Representation theorem of intuitionistic fuzzy LI -ideal which is generated by an intuitionistic fuzzy set is established. It is proved that the set consisting of all intuitionistic ...