Suppose <? denotes a class of totally ordered groups closed under taking subgroups and quotients by o-homomorphisms. We study the following classes: (1) Res (£?), the class of all lattice-ordered groups which are subdirect products of groups in C; (2) Hyp(C), the class of lattice-ordered groups in Res(C) having all their ¿-homomorphic images in Res(<?); Para(C), the class of lattice-ordered gro...

With the development of quantum computing, existing cryptography schemes based on classical cryptographic primitives will no longer be secure. Hence, cryptographers are designing post-quantum (PQC) schemes, and ideal lattice-based has emerged as a prime candidate. Today, becomes more mature, its performance an important optimization goal. In cryptography, polynomial arithmetic sampling most tim...

In this article we associate to every lattice ideal IL,ρ ⊂ K[x1, . . . , xm] a cone σ and a graph Gσ with vertices the minimal generators of the Stanley-Reisner ideal of σ. To every polynomial F we assign a subgraph Gσ(F ) of the graph Gσ. Every expression of the radical of IL,ρ, as a radical of an ideal generated by some polynomials F1, . . . , Fs gives a spanning subgraph of Gσ, the ∪ s i=1Gσ...

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 ...

Adviser: Carina Curto Neurons in the brain represent external stimuli via neural codes. These codes often arise from stimulus-response maps, associating to each neuron a convex receptive field. An important problem confronted by the brain is to infer properties of a represented stimulus space without knowledge of the receptive fields, using only the intrinsic structure of the neural code. How d...

We construct a diagram D⊲⊳, indexed by a finite partially ordered set, of finite Boolean 〈∨, 0, 1〉-semilattices and 〈∨, 0, 1〉-embeddings, with top semilattice 2, such that for any variety V of algebras, if D⊲⊳ has a lifting, with respect to the congruence lattice functor, by algebras and homomorphisms in V, then there exists an algebra U in V such that the congruence lattice of U contains, as a...