Notes on divisible MV-algebras

被引：0
作者：
Serafina Lapenta
Ioana Leuştean
机构：
[1] University of Salerno,Department of Mathematics
[2] University of Bucharest,Department of Computer Science, Faculty of Mathematics and Computer Science
来源：
Soft Computing | 2017年 / 21卷
关键词：
DMV-algebras; MV-algebras; Rational Łukasiewicz logic; Divisible hull; Rational polyhedra;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this notes, we study the class of divisible MV-algebras inside the algebraic hierarchy of MV-algebras with product. We connect divisible MV-algebras with Q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb Q$$\end{document}-vector lattices, we present the divisible hull as a categorical adjunction, and we prove a duality between finitely presented algebras and rational polyhedra.
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页码：6213 / 6223
页数：10
相关论文
共 21 条
  • [1] Baker KA(1968)Free vector lattices Canad J Math 20 58-66
  • [2] Beynon WM(1975)Duality theorem for finitely generated vector lattices Proc London Math Soc 31 114-128
  • [3] Chang CC(1958)Algebraic analysis of many valued logics Trans Am Math Soc 88 467-490
  • [4] Chang CC(1959)A new proof of the completeness of the Łukasiewicz axioms Trans Am Math Soc 93 74-80
  • [5] Diaconescu D(2015)The Riesz hull of a semisimple MV-algebra Mathematica Slovaka (special issue in honor of Antonio Di Nola) 65 801-816
  • [6] Leuştean I(2001)Product MV-algebras Mult-Valued Log 6 193-215
  • [7] Di Nola A(2003)MV-modules J Algebra 267 21-40
  • [8] Dvurečenskij A(2014)Łukasiewicz logic and Riesz spaces Soft Comput 18 2349-2363
  • [9] Di Nola A(2001)Rational Łukasiewicz logic and divisible MV-algebras Neural Netw World 10 579-584
  • [10] Flondor P(2013)Duality, projectivity and unification in Łukasiewicz logic and MV-algebras Ann Pure Appl Log 164 192-210
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