Permuting Tri-derivations in MV-algebras
Downloads
DOI:
https://doi.org/10.26637/mjm1102/003Abstract
An MV-algebra is an algebraic structure with a binary operation ⊕, a unary operation ′ and the constant 0 satisfying certain axioms. MV-algebras are the algebraic semantics of Lukasiewicz logic. This work includes a type of derivation research on MV-algebras. Our aim is to introduce the concept of permuting tri-derivation on MV-algebras and to discuss some results.
Keywords:
MV-algebra, permuting tri-derivation, fixed set, Boolean algebra, isotoneMathematics Subject Classification:
Mathematics- Pages: 142-150
- Date Published: 01-04-2023
- Vol. 11 No. 02 (2023): Malaya Journal of Matematik (MJM)
N. O. A LSHEHRI , Derivations of MV-algebras, Int. J. Math. Math. Sci., 312027(2010), 7 pp,
https://doi.org/10.1155/2010/312027. DOI: https://doi.org/10.1155/2010/312027
L. K. A RDEKANI , B. D AVVAZ , f-derivations and (f,g)-derivations of MV-algebras, J. algebraic syst., 1(2013),
–31.
M. A SHRAF , N. P ARVEEN , M. R. J AMAL , Traces of permuting n-derivations and commutativity of rings,
Southeast Asian Bull. Math., 38(2014), 321–332.
D. B USNEA , D. P ICIU , Localization of MV-algebras and lu-groups, Algebra Univers., 50(2003), 359–380. DOI: https://doi.org/10.1007/s00012-003-1848-7
Y. C¸ EVEN , M. A.O ZT URK , On f-derivations of lattices, Bull. Korean Math. Soc., 45(2008), 701–707. DOI: https://doi.org/10.4134/BKMS.2008.45.4.701
Y. C¸ EVEN , Symmetric bi-derivations of lattices, Quaest. Math., 32(2009), 241–245,
https://doi.org/10.2989/QM.2009.32.2.6.799. DOI: https://doi.org/10.2989/QM.2009.32.2.6.799
C. C HANG , Algebraic analysis of many valued logics, Trans. Am. Math. Soc., 88(1958), 467–490. DOI: https://doi.org/10.1090/S0002-9947-1958-0094302-9
R. C IGNOLI , I. M. L. D’O TTAVIANO , D. M UNDICI , Algebraic Foundations of Many valued Reasoning, Kluwer Academic Publ., Dordrecht, (2000), ). https://doi.org/10.1007/978-94-015-9480-6. DOI: https://doi.org/10.1007/978-94-015-9480-6
A. F O ˇ SNER , Prime and semiprime rings with symmetric skew 3-derivations, Aequationes mathematicae,
(2014), 191–200, https://doi.org/10.1007/s00010-013-0208-8 DOI: https://doi.org/10.1007/s00010-013-0208-8
A. F O ˇ SNER , Prime and semiprime rings with symmetric skew n-derivations, Colloquium Mathematicum, 134(2014), 245–253. DOI: https://doi.org/10.4064/cm134-2-8
S H. G HORBANI , L. T ORKZADEH , S. M OTAMED , (⊙,⊕)-Derivations and (⊖,⊙)-Derivations on
MV-algebras, Iranian Journal of Mathematical Sciences and Informatics, 8(2013), 75–90,
https://doi.org/10.7508/ijmsi.2013.01.008
D. M UNDICI , Interpretation of AF C*-algebras in Lukasiewicz sentential calculus, Journal of Functional
Analysis, 65(1986), 15–63. DOI: https://doi.org/10.1016/0022-1236(86)90015-7
D. M UNDICI , MV-algebras are categorically equivalent to bounded commutative BCK-algebras,Math.
Japon., 31(1986), 889–894. DOI: https://doi.org/10.1037/024253
M. A. ¨ O ZT ¨ URK , H. Y AZARLI K. H. K IM , Permuting tri-derivations in lattices, Quaestiones Mathematicae,32(2009), 415–425, https://doi.org/10.2989/QM.2009.32.3.10.911. DOI: https://doi.org/10.2989/QM.2009.32.3.10.911
M. A. ¨ O ZT ¨ URK , Permuting tri-derivations in prime and semi-prime rings , East Asian Math. J., 15(1999), 177–190.
E. C. P OSNER , Derivation in prime rings, Proc. Am. Math. Soc., 8(1957), 1093–1100. DOI: https://doi.org/10.1090/S0002-9939-1957-0095863-0
G. S ZASZ , Derivations of lattices, Acta Scientiarum Mathematicarum, 37(1975), 149–154.
X. L. X IN , T. Y. L I , J. H. L U , On derivations of lattices, Information Sciences, 178(2008), 307–316,
https://doi.org/10.1016/j.ins.2007.08.018. DOI: https://doi.org/10.1016/j.ins.2007.08.018
X. L. X IN , The fixed set of a derivation in lattices, Fixed Point Theory and Applications, 1(2012), 218,
https://doi.org/10.1186/1687-1812-2012-218. DOI: https://doi.org/10.1186/1687-1812-2012-218
H. Y AZARLI , A note on derivations in MV-algebras, Miskolc Mathematical Notes, 14(2013), 345–354,
https://doi.org/10.18514/MMN.2013.420. DOI: https://doi.org/10.18514/MMN.2013.420
- NA
Metrics
Published
How to Cite
Issue
Section
License
Copyright (c) 2023 Damla Yılmaz, Bijan Davvaz, Hasret Yazarlı
This work is licensed under a Creative Commons Attribution 4.0 International License.
