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Year 2019, Volume: 9 Issue: 3, 554 - 562, 01.09.2019

Abstract

References

  • Birkhoof, G., (1940), Lattice Theory, Amer. Math. Soc., New York.
  • Balbes, R. and Dwinger, P., (1974), Distributive Lattices, University of Missouri Press, Columbia, USA.
  • Bell, A. J., (2003), The co-information lattice, in: 4th International Sympo- sium on Independent Com- ponent Analysis and Blind Signal Separation (ICA2003), Nara, Japan, pp. 921-926.
  • Carpineto, C. and Romano, G., (1996), Information retrieval through hybrid naviga- tion of lattice representations, Int. J. Human Computers Studies, 45, pp. 553-578.
  • Sandhu, R.S., (1996), Role hierarchies and constraints for lattice-based access con- trols, in: Proceedings of the 4th European Symposium on Research in Computer Security, Rome, Italy, pp. 65-79.
  • Durfee, G., (2002), Cryptanalysis of RSA using algebraic and lattice methods, A dissertation submitted to the Department of Computer Science and the committee on graduate studies of Stanford University, pp. 1-114.
  • Honda, A. and Grabisch, M., (2006), Entropy of capacities on lattices and set systems, Inform. Sci., 176, pp. 3472-3489.
  • Posner, E., (1957), Derivations in prime rings, Proc. Am. Math. Soc., 8, pp. 1093-1100.
  • Bell, H. E. and Kappe, L. C., (1989), Rings in which derivations satisfy certain algebraic conditions, Acta Math. Hungar., 53 (3-4), pp. 339-346.
  • Bresar, M., (1991), On the distance of the composition of the two derivations to the generalized deriva- tions, Glasgow Math. J., 33 (1), pp. 89-93.
  • Hvala, B., (1998), Generalized derivations in rings, Common. Alg., 26 (4), pp. 1147-1166.
  • Arga¸c, N. and Albas, E., (2004), Generalized derivations of prime rings, Algebra Coll., 11, pp. 399-410.
  • G¨olba¸si, ¨O. and Kaya, K., (2006), On Lie ideal with generalized derivations, Siberian. Math. J., 47 (5), pp. 862-866.
  • Jana, C., Senapati, T. and Pal, M., (2016), (∈, ∈ ∨q)-intuitionistic fuzzy BCI-subalgebras of BCI- algebra, Journal of Intelligent and Fuzzy systems, 31, pp. 613-621.
  • Jana, C., Senapati, T., Bhowmik, M. and Pal, M., (2015), On intuitionistic fuzzy G-subalgebras ofG-algebras, Fuzzy Information and Engineering, 7, pp. 195-209.
  • Jana, C. and Pal, M., (2016), Applications of new soft intersection set on groups, Annals of Fuzzy Mathematics and Informatics, 11 (6), pp. 923-944.
  • Jana, C., (2015), Generalized (Γ, Υ)-derivation on subtraction algebras, Journal of Mathematics and Informatics, 4, pp. 71-80.
  • Jana, C. and Pal, M., (2017), Application of (α, β)-soft intersectional sets on BCK/BCI-algebras, Int. J. Intelligent Systems Technologies and Applications, 16 (3), pp. 269-288.
  • Jana, C., Pal, M. and Saied, A. B., (2017), (∈, ∈ ∨q)-bipolar fuzzy BCK/BCI-algebras, Missouri Journal of Mathematical Scienc, (accepted).
  • Jana, C., Senapati, T. and Pal, M., (2015), Derivation, f -derivation and generalized derivation of KU S- algebras, Cogent Mathematics, 2, pp. 1-12.
  • Jana, C., Senapati, T. amd Pal, M. , (2017), On t-derivation of complicated subtraction algebras, Journal of Discrete Mathematical Sciences and Cryptography, (accepted).
  • Xin, X. L., Li, T. Y. and Lu, J. H., (2008), On Derivations of Lattices, Inform. Sci., 178, pp. 307-316.
  • Maksa, G. Y., (1980), A remark on symmetric biadditive functions having nonnegative diagonalization, Glasnik Math, 15 (35), pp. 279-282.
  • Maksa, G. Y., (1989), On the trace of symmetric bi-derivations, C.R. Math. Rep. Acad. Sci. Canada, 9, pp. 303-307.
  • Ozturk, M.A. and Sapancy, M., (1999), On generalized symmetric bi-derivations in prime rings, East
  • Asian Mathematical Journal, 15 (2), pp. 165-176. Sapancy, M., Ozturk, M. A. and Jun, Y. B., (1999), Symmetric bi-derivations on prime rings, East Asian
  • Mathematical Journal, 15 (1), pp. 105-109. Vukman, J., (1989), Symmetric bi-derivations on prime and semi-prime rings, Aequationes Mathemati- cae, 38, pp. 245-254.
  • Vukman, J., (1990), Two results concerning symmetric bi-derivations on prime rings, Aequationes Math- ematicae, 40, pp. 181-189.
  • C¸ ven, Y., (2009), Symmetric bi-derivations of lattices, Quaest. Math., 32, pp. 241-245.

SYMMETRIC BI-T-DERIVATION OF LATTICES

Year 2019, Volume: 9 Issue: 3, 554 - 562, 01.09.2019

Abstract

In this paper, the notion of a new kind of derivation is introduced for a lattice L;_;^ , called symmetric bi-T-derivations on L as a generalization of derivation of lattices and characterized some of its related properties. Some equivalent conditions provided for a lattice L with greatest element 1 by the notion of isotone symmetric bi-T-derivation on L. By using the concept of isotone derivation, we characterized the modular and distributive lattices by the notion of isotone symmetric bi-T-derivation on L.

References

  • Birkhoof, G., (1940), Lattice Theory, Amer. Math. Soc., New York.
  • Balbes, R. and Dwinger, P., (1974), Distributive Lattices, University of Missouri Press, Columbia, USA.
  • Bell, A. J., (2003), The co-information lattice, in: 4th International Sympo- sium on Independent Com- ponent Analysis and Blind Signal Separation (ICA2003), Nara, Japan, pp. 921-926.
  • Carpineto, C. and Romano, G., (1996), Information retrieval through hybrid naviga- tion of lattice representations, Int. J. Human Computers Studies, 45, pp. 553-578.
  • Sandhu, R.S., (1996), Role hierarchies and constraints for lattice-based access con- trols, in: Proceedings of the 4th European Symposium on Research in Computer Security, Rome, Italy, pp. 65-79.
  • Durfee, G., (2002), Cryptanalysis of RSA using algebraic and lattice methods, A dissertation submitted to the Department of Computer Science and the committee on graduate studies of Stanford University, pp. 1-114.
  • Honda, A. and Grabisch, M., (2006), Entropy of capacities on lattices and set systems, Inform. Sci., 176, pp. 3472-3489.
  • Posner, E., (1957), Derivations in prime rings, Proc. Am. Math. Soc., 8, pp. 1093-1100.
  • Bell, H. E. and Kappe, L. C., (1989), Rings in which derivations satisfy certain algebraic conditions, Acta Math. Hungar., 53 (3-4), pp. 339-346.
  • Bresar, M., (1991), On the distance of the composition of the two derivations to the generalized deriva- tions, Glasgow Math. J., 33 (1), pp. 89-93.
  • Hvala, B., (1998), Generalized derivations in rings, Common. Alg., 26 (4), pp. 1147-1166.
  • Arga¸c, N. and Albas, E., (2004), Generalized derivations of prime rings, Algebra Coll., 11, pp. 399-410.
  • G¨olba¸si, ¨O. and Kaya, K., (2006), On Lie ideal with generalized derivations, Siberian. Math. J., 47 (5), pp. 862-866.
  • Jana, C., Senapati, T. and Pal, M., (2016), (∈, ∈ ∨q)-intuitionistic fuzzy BCI-subalgebras of BCI- algebra, Journal of Intelligent and Fuzzy systems, 31, pp. 613-621.
  • Jana, C., Senapati, T., Bhowmik, M. and Pal, M., (2015), On intuitionistic fuzzy G-subalgebras ofG-algebras, Fuzzy Information and Engineering, 7, pp. 195-209.
  • Jana, C. and Pal, M., (2016), Applications of new soft intersection set on groups, Annals of Fuzzy Mathematics and Informatics, 11 (6), pp. 923-944.
  • Jana, C., (2015), Generalized (Γ, Υ)-derivation on subtraction algebras, Journal of Mathematics and Informatics, 4, pp. 71-80.
  • Jana, C. and Pal, M., (2017), Application of (α, β)-soft intersectional sets on BCK/BCI-algebras, Int. J. Intelligent Systems Technologies and Applications, 16 (3), pp. 269-288.
  • Jana, C., Pal, M. and Saied, A. B., (2017), (∈, ∈ ∨q)-bipolar fuzzy BCK/BCI-algebras, Missouri Journal of Mathematical Scienc, (accepted).
  • Jana, C., Senapati, T. and Pal, M., (2015), Derivation, f -derivation and generalized derivation of KU S- algebras, Cogent Mathematics, 2, pp. 1-12.
  • Jana, C., Senapati, T. amd Pal, M. , (2017), On t-derivation of complicated subtraction algebras, Journal of Discrete Mathematical Sciences and Cryptography, (accepted).
  • Xin, X. L., Li, T. Y. and Lu, J. H., (2008), On Derivations of Lattices, Inform. Sci., 178, pp. 307-316.
  • Maksa, G. Y., (1980), A remark on symmetric biadditive functions having nonnegative diagonalization, Glasnik Math, 15 (35), pp. 279-282.
  • Maksa, G. Y., (1989), On the trace of symmetric bi-derivations, C.R. Math. Rep. Acad. Sci. Canada, 9, pp. 303-307.
  • Ozturk, M.A. and Sapancy, M., (1999), On generalized symmetric bi-derivations in prime rings, East
  • Asian Mathematical Journal, 15 (2), pp. 165-176. Sapancy, M., Ozturk, M. A. and Jun, Y. B., (1999), Symmetric bi-derivations on prime rings, East Asian
  • Mathematical Journal, 15 (1), pp. 105-109. Vukman, J., (1989), Symmetric bi-derivations on prime and semi-prime rings, Aequationes Mathemati- cae, 38, pp. 245-254.
  • Vukman, J., (1990), Two results concerning symmetric bi-derivations on prime rings, Aequationes Math- ematicae, 40, pp. 181-189.
  • C¸ ven, Y., (2009), Symmetric bi-derivations of lattices, Quaest. Math., 32, pp. 241-245.
There are 29 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

C. Jana This is me

K. Hayat This is me

M. Pal This is me

Publication Date September 1, 2019
Published in Issue Year 2019 Volume: 9 Issue: 3

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