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山东大学学报（理学版） ›› 2016, Vol. 51 ›› Issue (8): 53-60.doi: 10.6040/j.issn.1671-9352.0.2015.610

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Monadic MV-代数上的微分

刘慧珍1,辛小龙1*,王军涛1   

  1. 西北大学数学学院, 陕西 西安 710127
  • 收稿日期:2015-12-17 出版日期:2016-08-20 发布日期:2016-08-08
  • 通讯作者: 辛小龙(1955— ), 男, 教授, 博士生导师, 研究方向为逻辑代数、超代数、不确定性理论. E-mail:xlxin@nwu.edu.cn E-mail:1320746211@qq.com
  • 作者简介:刘慧珍(1989— ), 女, 硕士生, 研究方向为逻辑代数. E-mail:1320746211@qq.com
  • 基金资助:
    国家自然科学基金资助项目(11571281)

On derivations of monadic MV-algebras

LIU Hui-zhen1, XIN Xiao-long1*, WANG Jun-tao1   

  1. School of Mathematics, Northwest University, Xian 710127, Shaanxi, China
  • Received:2015-12-17 Online:2016-08-20 Published:2016-08-08

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摘要： 在Monadic MV-代数(M,∃)上引入并研究了M-微分。定义并研究了Monadic MV-代数(M,∃)上的强M-微分和正则M-微分,利用强M-微分,给出了一个MV-代数成为布尔代数的等价刻画,并给出了正则M-微分成为保序M-微分的等价刻画。进一步地,在Monadic MV-代数(M,∃)上定义不动点集合Fd∃,证明了若d为保序微分时,Monadic MV-代数上的不动点之集为M的格理想。随后,在Monadic MV-代数上定义并研究了可加微分,从而得到了一些关于可加微分的重要性质。最后,在微分Monadic MV-代数(M,∃,d)上定义了Monadic微分理想,并对其进行了刻画,而且研究了(M,∃,d)上所有Monadic微分理想组成的集合ID(M)的代数结构。

关键词: MV-代数, 微分, 微分理想, 不动点之集, monadic算子

Abstract: We define the notion of M-derivations on monadic MV-algebras(M,∃)and discuss some properties of it. Based on it, the notions of the strong M-derivations and regular M-derivations are introduced. By use of strong M-derivations, we give some equivalent conditions in which a MV-algebra becomes a boolean algebra. Next, some characterizations about the isotone M-derivations in monadic MV-algebras are provided by regular M-derivations. Moreover, the notion of the fixed set of a derivation in monadic MV-algebras is introduced and discussed. The notion of additive derivations of monadic MV-algebras are given and some of its properties are investigated. Also, we prove that an additive derivation of linearly ordered monadic MV-algebras is isotone. Finally, monadic differential ideals of monadic MV-algebras are studied. In particular, algebraic structures of the set ID(M)of all monadic differential ideals on regular monadic MV-algebras are researched.

Key words: MV-algebra, derivation, the fixed set, differential ideal, monadic operator

中图分类号: 

  • O155
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