GENERALIZED (f; g)-DERIVATIONS OF LATTICES

Mustafa Aşcı; Şahinceran

EN

GENERALIZED (f; g)-DERIVATIONS OF LATTICES

Abstract

In this paper as a generalization of derivation and f -derivation ona lattice we introduce the notion of generalized (f, g)-derivation of a lattice.We give illustrative example. If the function g is equal to the function f thenthe generalized (f, g)-derivation is the f -derivation defined in [8]. Also if wechoose the function f and g the identity functions both then the derivation wedefine coincides with the derivation defined in [22]

Keywords

Lattice, Derivation, (f, g)-derivation

References

A. J. Bell, The co-information lattice, 4th Int. Symposium on Independent ComponentvAnal- ysis and Blind Signal Seperation (ICA2003), Nara, Japan, 2003, 921–926.
A. Honda and M. Grabisch, Entropy of capacities on lattices and set systems, Inform. Sci. 176 (2006), no. 23, 3472–3489.
Asci, M., Kecilioglu O., Davvaz B. On Symmetric f bi-derivations of Lattices. J. Combin. Math. Combin. Comput. 83, (2012), pp. 243-253..
Asci, M., Kecilioglu O., Ceran S¸. Permuting Tri (f,g) derivations on Lattices. Ann. Fuzzy Math. Inform. (AFMI). Vol 1, No.2 (2011), pp. 189-196. .
Ceran, S¸. Asci, M. Symmetric bi-(σ, τ ) derivations of prime and semi prime gamma rings. Bull. Korean Math. Soc. 43 (2006), no. 1, 9–16.
C. Carpineto and G. Romano, Information retrieval through hybrid navigation of lattice representations, International Journal of Human-Computers Studies 45 (1996), 553–578.
C. Degang, Z. Wenxiu, D. Yeung, and E. C. C. Tsang, Rough approximations on a complete completely distributive lattice with applications to generalized rough sets, Inform. Sci. 176 (2006), no. 13, 1829–1848.
C¸ even, Y. ¨Ozt¨urk, M. A. On f-derivations of lattices. Bull. Korean Math. Soc. 45 (2008), no. 4, 701–707.
C¸ even, Y. Symmetric bi derivations of Lattices, Quaestiones Mathematicae, 32(2009), 1-5
C¸ even, Y. ¨Ozt¨urk, M. A. Some properties of symmetric bi-(σ, τ )-derivations in near-rings. Commun. Korean Math. Soc. 22 (2007), no. 4, 487–491.

Davey, B. A.; Priestley, H. A. Introduction to lattices and order. Second edition. Cambridge University Press, New York, 2002. xii+298 pp. ISBN: 0-521-78451-4
E. Posner, Derivations in prime rings, Proc. Amer. Math. Soc. 8 (1957), 1093–1100.
Ferrari, Luca On derivations of lattices. Pure Math. Appl. 12 (2001), no. 4, 365–382.
G. Durfee, Cryptanalysis of RSA using algebraic and lattice methods, A dissertation submit- ted to the department of computer sciences and the committe on graduate studies of Stanford University (2002), 1–114.
G. Birkhoof, Lattice Theory, American Mathematical Society, New York, 1940.
H. E. Bell and L. C. Kappe, Rings in which derivations satisfy certain algebraic conditions, Acta Math. Hungar. 53 (1989), no. 3-4, 339–346.
J. Zhan and Y. L. Liu, On f-derivations of BCI-algebras, Int. J. Math. Math. Sci. (2005), no. 11, 1675–1684.
Ozbal, S.A, Firat, A. Symmetric f bi Derivations of Lattices. Ars Combin. 97 (2010) in press. [19] R. Balbes and P. Dwinger, Distributive Lattices, University of Missouri Press, Columbia, Mo., 1974.
R. S. Sandhu, Role hierarchies and constraints for lattice-based access controls, Proceedings of the 4th Europan Symposium on Research in Computer Security, Rome, Italy, 1996, 65–79. [21] Sz´asz, G. Derivations of lattices. Acta Sci. Math. (Szeged) 37 (1975), 149–154.
X. L. Xin, T. Y. Li, and J. H. Lu, On derivations of lattices, Inform. Sci. 178 (2008), no. 2, 307–316. [23] Y. B. Jun and X. L. Xin, On derivations of BCI-algebras, Inform. Sci. 159 (2004), no. 3-4, 167–176. Pamukkale University Science and Arts Faculty Department of Mathematics Kınıklı Denizli TURKEY
E-mail address: mustafa.asci@yahoo.com
E-mail address: sceran@pau.edu.tr

Details

Primary Language

English

Subjects

-

Journal Section

-

Authors

Mustafa Aşcı This is me

Şahinceran This is me

Publication Date

December 1, 2013

Submission Date

March 9, 2015

Acceptance Date

-

Published in Issue

Year 2013 Volume: 1 Number: 2

IZ

https://izlik.org/JA92GK76AD

Vancouver

1.Mustafa Aşcı, Şahinceran . GENERALIZED (f; g)-DERIVATIONS OF LATTICES. Math. Sci. Appl. E-Notes [Internet]. 2013 Dec. 1;1(2):56-62. Available from: https://izlik.org/JA92GK76AD