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On f derivations and g derivations of MV-algebras

FENG Min1, XIN Xiao-long1*, LI Yi-jun1,2   

  1. 1. School of Mathematics, Northwest University, Xian 710127, Shaanxi, China;
    2. College of Science, Xian Shiyou University, Xian 710065, Shaanxi, China
  • Received:2014-02-10 Online:2014-06-20 Published:2014-06-14

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Abstract: 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 between f derivations and g derivations are discussed.

Key words: Boolean algebra, g derivation, f derivation, MV-algebra, ideal

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