%0 Journal Article
%T Monadic MV-代数上的微分<br>On derivations of monadic MV-algebras
%A 刘慧珍
%A 辛小龙
%A 王军涛&lt
%A br&gt
%A LIU Hui-zhen
%A XIN Xiao-long
%A WANG Jun-tao
%J 山东大学学报（理学版）
%D 2016
%R 10.6040/j.issn.1671-9352.0.2015.610
%X 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。<br>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
%K MV-代数
%K 微分
%K 微分理想
%K 不动点之集
%K monadic算子
%K &lt
%K br&gt
%K MV-algebra
%K derivation
%K the fixed set
%K differential ideal
%K monadic operator
%U http://lxbwk.njournal.sdu.edu.cn/CN/10.6040/j.issn.1671-9352.0.2015.610