Monadic MV-代数上的微分

On derivations of monadic MV-algebras

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。

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.