JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2016, Vol. 51 ›› Issue (8): 53-60.doi: 10.6040/j.issn.1671-9352.0.2015.610

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On derivations of monadic MV-algebras

LIU Hui-zhen1, XIN Xiao-long1*, WANG Jun-tao1   

  1. School of Mathematics, Northwest University, Xian 710127, Shaanxi, China
  • Received:2015-12-17 Online:2016-08-20 Published:2016-08-08

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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.

Key words: MV-algebra, derivation, the fixed set, differential ideal, monadic operator

CLC Number: 

  • O155
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