MV-代数上的广义微分

On Generalized Derivations of MV-algebras

在MV-代数上引入了广义微分的概念,研究了MV-代数广义微分的相关性质。进一步引入了保序广义微分的概念。给出了MV-代数上的保序广义微分的若干等价条件。进一步,在MV-代数M上引入了广义微分D的不动点集FixD(M),得到若D是保序广义微分,则FixD(M)是M的理想与格理想。进而通过广义微分的不动点集刻画了布尔代数和线性布尔代数。

In this paper, we introduce the notion of generalized derivations in MV-aigebras ana alscuss some properties. We also define the isotone generalized derivation and make researches about some equivalent conditions of isotone generalized derivation. Moreover we define the set FixD （M） and prove that the fixed set FixD（M） is an ideal and lattice ideal of M if D is an isotone generalized derivation in a MV-algebra M. And we establish a characterization of a Boolean algebra and a liner Boolean algebra by the fixed set of generalized derivation, respectively.