Some results on derivations of MV-algebras

被引：0
作者：
Jun-tao Wang
Peng-fei He
Yan-hong She
机构：
[1] Xi’an Shiyou University,School of Science
[2] Shaanxi Normal University,School of Mathematics and Statistics
来源：
Applied Mathematics-A Journal of Chinese Universities | 2023年 / 38卷
关键词：
MV-algebra; derivation; fixed point set; ideal; Boolean algebra; 06B35; 06B99;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, we review some of their related properties of derivations on MV-algebras and give some characterizations of additive derivations. Then we prove that the fixed point set of Boolean additive derivations and that of their adjoint derivations are isomorphic. In particular, we prove that every MV-algebra is isomorphic to the direct product of the fixed point set of Boolean additive derivations and that of their adjoint derivations. Finally we show that every Boolean algebra is isomorphic to the algebra of all Boolean additive (implicative) derivations. These results also give the negative answers to two open problems, which were proposed in [Fuzzy Sets and Systems, 303(2016), 97–113] and [Information Sciences, 178(2008), 307–316].
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页码：126 / 143
页数：17
相关论文
共 52 条
  • [1] Ardekani L K(2015) ( Journal of Multiple-valued Logic and Soft Computing 25 491-510
  • [2] Davvaz B(1958)) Trans Amer Math Soc 88 467-490
  • [3] Chang C C(1959)Algebraic analysis of many-valued logic Trans Amer Math Soc 93 74-80
  • [4] Chang C C(1997)A new proof of the completeness of the Lukasiewicz axioms Stud Log 58 79-97
  • [5] Cignoli R(2017)An elementary proof of Chang’s completeness theorem for the infinite-valued calculus of Lukasiewicz J Contemp Mathemat Anal 57 166-174
  • [6] Mundici D(2014)Generalized (Jordan) left derivations on rings associated with an element of rings J Intell Fuzzy Syst 27 1557-1565
  • [7] Davvaz B(2014)Stabilizer theory in MV-algebras Univ Politehn Bucharest Sci Bull Ser A Appl Math Phys 76 53-62
  • [8] Ardekani L K(2003)On obstinate ideals in MV-algebras Neural Netw World 5 467-480
  • [9] Forouzesh F(2013)Many valued logics and semirings Iran J Math Sci Inform 8 75-90
  • [10] Eslami E(2016)(⊙, ⊕) Fuzzy Sets Syst 303 97-113
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