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Structures grammaticales dans le français mathématique : II - (suite et fin)

Aarne Ranta (1997)

Mathématiques et Sciences Humaines

Un système de règles grammaticales est présenté pour analyser un fragment du français permettant l'expression de théorémes et de preuves mathématiques. Pour cet objectif, on développe une version de la grammaire de Montague, avec des catégories syntaxiques relatives au contexte et aux domaines d'individus. Ce système peut être interprété dans la théorie constructive des types de Martin-Löf. Il est appliqué, d'abord, au français sans symboles mathématiques, avec une attention spéciale aux restrictions...

Subdirectly irreducible MV-algebras

Hernando Gaitan (2003)

Czechoslovak Mathematical Journal

In this note we characterize the one-generated subdirectly irreducible MV-algebras and use this characterization to prove that a quasivariety of MV-algebras has the relative congruence extension property if and only if it is a variety.

Subgroups of the Baer–Specker group with few endomorphisms but large dual

Andreas Blass, Rüdiger Göbel (1996)

Fundamenta Mathematicae

Assuming the continuum hypothesis, we construct a pure subgroup G of the Baer-Specker group ℤ ℵ 0 with the following properties. Every endomorphism of G differs from a scalar multiplication by an endomorphism of finite rank. Yet G has uncountably many homomorphisms to ℤ.

Submodule of free Z-module

Yuichi Futa, Hiroyuki Okazaki, Yasunari Shidama (2013)

Formalized Mathematics

In this article, we formalize a free Z-module and its property. In particular, we formalize the vector space of rational field corresponding to a free Z-module and prove formally that submodules of a free Z-module are free. Z-module is necassary for lattice problems - LLL (Lenstra, Lenstra and Lov´asz) base reduction algorithm and cryptographic systems with lattice [20]. Some theorems in this article are described by translating theorems in [11] into theorems of Z-module, however their proofs are...

Sufficient conditions for a T-partial order obtained from triangular norms to be a lattice

Lifeng Li, Jianke Zhang, Chang Zhou (2019)

Kybernetika

For a t-norm T on a bounded lattice ( L , ≤ ) , a partial order ≤ T was recently defined and studied. In [11], it was pointed out that the binary relation ≤ T is a partial order on L , but ( L , ≤ T ) may not be a lattice in general. In this paper, several sufficient conditions under which ( L , ≤ T ) is a lattice are given, as an answer to an open problem posed by the authors of [11]. Furthermore, some examples of t-norms on L such that ( L , ≤ T ) is a lattice are presented.

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