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On derivations and their fixed point sets in residuated lattices

机译：剩余格中的导数及其不动点集

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摘要

The main goal of this paper is to investigate derivations in residuated lattices and characterize some special types of residuated lattices in terms of derivations. In the paper, we discuss related properties of some particular derivations and give some characterizations of (good) ideal derivations. Then we obtain that the fixed point set of good ideal derivations is still a residuated lattice. Also, we prove that the set of all ideal derivation filters on residuated lattices with good ideal derivations can form a complete Heyting algebra, which is isomorphic to the lattice of all filters in the fixed point set for good ideal derivations. Moreover, we study principal ideal derivations and their adjoint derivations. Finally, we get that the fixed point set of principal ideal derivations and that of their adjoint derivations are order isomorphism. In particular, using the fixed point set of principal ideal derivations, we give characterizations of Heyting algebras and linearly ordered Heyting algebras. (C) 2016 Elsevier B.V. All rights reserved.
机译：本文的主要目的是研究残差格的导数，并根据导数来表征残格的某些特殊类型。在本文中，我们讨论了某些特定导数的相关性质，并给出了（良好）理想导数的一些特征。然后我们得到，良好理想导数的不动点集仍然是剩余格。同样，我们证明，在具有良好理想导数的剩余格上的所有理想导数滤波器的集合可以形成完整的Heyting代数，该代数与在固定点集中所有滤波器的晶格同构，以实现良好的理想导数。此外，我们研究了主要的理想派生及其伴随派生。最终，我们得到主要理想导数及其伴随导数的不动点集是阶同构。特别是，使用主要理想导数的不动点集，我们给出了Heyting代数和线性有序Heyting代数的刻画。 （C）2016 Elsevier B.V.保留所有权利。

著录项

  • 来源
    《Fuzzy sets and systems》 |2016年第15期|97-113|共17页
  • 作者

    He Pengfei; Xin Xiaolong; Zhan Jianming;

  • 作者单位

    Shaanxi Normal Univ, Sch Math & Informat Sci, Xian 710119, Peoples R China|Northwest Univ, Coll Math, Xian 710127, Peoples R China;

    Northwest Univ, Coll Math, Xian 710127, Peoples R China;

    Hubei Univ Nationalities, Dept Math, Enshi 445000, Peoples R China;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Residuated lattice; Ideal derivation; Heyting algebra; Fixed point set;

    机译：剩余格;理想导数;Heyting代数;固定点集;

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