MV-代数上的f导子和g导子

On f derivations and g derivations of MV-algebras

利用MV-代数的自同态,将MV-代数上的(⊙,)导子和(Θ,⊙)导子进行了推广,引入了f导子和g导子,研究了它们的相关性质。得到了g导子d的不动点集Fd(M)g是M的理想;保序的f导子d的不动点集Fd(M)f是M的理想,并用g导子的相关性质刻画了布尔代数和线性布尔代数。最后讨论了f导子和g导子之间的关系。

Using the endomorphism of MV-algebra, the notions of f derivations and g derivations of MV-algebras are introduced, which extend （⊙, ）-derivations and （ ,⊙）-derivations, respectively.And some related properties are investigated.Moreover, the set Fd （M） g of all fixed points for a g derivation d is proved to be an ideal of M and the set Fd （M） f of all fixed points for an isotone f derivation d is proved to be an ideal of M.Furthermore, characterizations of Boolean algebras and linear Boolean algebras are derived by properties of g derivations.Finally, the relationships be-tween f derivations and g derivations are discussed.