JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2017, Vol. 52 ›› Issue (11): 95-99.doi: 10.6040/j.issn.1671-9352.0.2017.035

Previous Articles     Next Articles

Characterizations and properties of triple-δ-derivation in Boolean algebra

LIU Li-jun1,2   

  1. 1. School of Mathematics and Computer Science, Shaanxi University of Technology, Hanzhong 723000, Shaanxi, China;
    2. College of Mathematics and Information Science, Shaanxi Normal University, Xian 710119, Shaanxi, China
  • Received:2017-02-10 Online:2017-11-20 Published:2017-11-17

PDF (PC)

287

Abstract: The concept of triple-δ-derivation in the Boolean algebra is introduced, and some properties and characteristies of triple-δ-derivation are obtained. Especially, the characterization theorem for the isotone triple-δ-derivation is given in the Boolean algebra. The results of this study not only enrich the derivation theory of Boolean algebra, but also provide a theoretical basis for the study of derivations on lattices.

Key words: Boolean algebra, lattice, triple-δ-derivation, derivation

CLC Number: 

  • O159
[1] POSNER E.Derivations in prime rings[J]. Proc Amer Math Soc, 1957, 8(6):1093-1100.
[2] SZÁSZ. Derivations of lattices[J]. Acta Sci Math Szeged, 1975, 37(3):149-154.
[3] XIN Xiaolong. On derivationsof lattices[J]. Inform Sci, 2008, 178(2):307-316.
[4] CEVEN Y,OZTURK M. On f-derivations of lattices[J]. Bull Korean Math Soc, 2008, 45(4):701-707.
[5] 李毅君,辛小龙. λ-格的微分[J]. 计算机工程与应用, 2010,46(6):46-47. LI Yijun, XIN Xiaolong. Differential of λ-lattice[J]. Computer engineering and Applications, 2010, 46(6):46-47.
[6] ALSHEHRI N. Derivations of MV-algebras[J]. Int J Math Math Sci, 2010. doi:10.1155/2010/312027.
[7] 孙道德,王敏生. 离散数学[M].安徽:中国科学技术大学出版社,2010. SUN Desheng, WANG Minsheng. Discrete mathematics[M]. Anhui: University of Science and Technology China Press, 2010.
[8] OZTURK M, YAZARH H. Permuting tri-derivations in lattices[J]. Quaest Math, 2009, 32(3):415-425.
[1] ZHANG En-sheng. Composition and structure on attribute reduction of interval-set concept lattices [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(8): 17-24.
[2] LIU Chun-hui. On(∈,∈∨q(λ, μ))-fuzzy LI-ideals in lattice implication algebras [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(2): 65-72.
[3] PENG Jia-yin. Falling fuzzy filters on residuated lattices [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(2): 52-64.
[4] SHAO Yong. Semilattice-ordered completely regular periodic semigroups [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(10): 1-5.
[5] LIU Li-jun. Characterizations of n-fold positive implicative filter in residuated lattice [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(8): 48-52.
[6] LI Jin-hai, WU Wei-zhi. Granular computing approach for formal concept analysis and its research outlooks [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(7): 1-12.
[7] HUANG Tao-lin, NIU Jiao-jiao, LI Jin-hai. Reduct updating method in a dynamic formal context based on granular discernibility attribute matrix [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(7): 13-21.
[8] LUO Peng, YANG Xiao-yuan. Identity-based encryption in multiple PKG environment based on ring signature [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(6): 64-68.
[9] LIU Lin, WEI Ling, QIAN Ting. Three-way rules extraction in formal decision contexts with confidence [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(2): 101-110.
[10] CHEN Xue, WEI Ling, QIAN Ting. Attribute reduction in formal decision contexts based on AE-concept lattices [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(12): 95-103.
[11] LIANG Ying, CUI Yan-li, WU Hong-bo. Properties of residuated lattice of deduction systems set algebra in BL system [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(11): 65-70.
[12] LIU Chun-hui. Lattice of(,∨(-overq))-fuzzy filters in a BL-algebra [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(10): 104-110.
[13] LIU Hui-zhen, XIN Xiao-long, WANG Jun-tao. On derivations of monadic MV-algebras [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(8): 53-60.
[14] QIAO Xi-min, WU Hong-bo. 〈,(-overQ)〉-fuzzy filter and its characterization of the non-commutative residual lattices on the interval sets [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(2): 102-107.
[15] LIN Ping-feng. Non-solvabla elements of semigroup PΓ(Λ×Λ)of binary relations determined by the semilattice Γ on the set Λ [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(2): 12-15.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd