The Theory of Derivations in Almost Distributive Lattices
Abstract
In this paper, we introduce the concept of a derivation in anAlmost Distributive Lattice (ADL) and derive some important properties of derivations in ADLs. Also we introduce the concepts of a principal derivation, an isotone derivation and the xed set of a derivation. We derive important results on derivations in Heyting ADLs.
References
[1] N.O.Alshehri. Generalized derivations of lattices, Int. J. Contemp. Math. Sciences, 5(13)(2010), 629-640.
[2] H.E.Bell and L.C.Kappe. Ring in which derivations satisfy certain algebraic conditions, Acta Math. Hung., 53(3-4)(1989), 339-346.
[3] Y. Ceven and M. A. Ozturk. On f-derivations of lattice, Bull. Korean Math. Soc., 45(4)(2008), 701-707.
[4] Y. Ceven. Symmetric Bi-derivations of lattice, Quaestiones Mathematicae, 32(2)(2009), 241-245.
[5] K.Kaya. Prime rings with a derivations, Bull. Mater. Sci. Eng,16(1987), 63-71.
[6] K. H. Kim. Symmetric Bi-f-derivations in lattices, Int. J. Math. Archive, 3(10)(2012), 3676-3683.
[7] M. Asci and S. Ceran. Generalized (f,g)-Derivations of Lattices, Math. Sci. Appl., E-notes, 1(2)(2013), 56-62.
[8] M. A. ztrk, H. Yazarli and K. H. Kim. Permuting tri-derivations in lattices, Quaestiones Mathematcae, 32(3)(2009), 415-425.
[9] E. Posner. Derivations in prime rings, Proc. Amer. Math. Soc., 8(6)(1957), 1093-1100.
[10] Rao, G.C. Almost Distributive Lattices. Doctoral Thesis, Dept. of Mathematics, Andhra University, Visakhapatnam. 1980
[11] Rao, G.C. B. Assaye and M. V. Ratna Mani. Heyting Almost Distributive Lattices, Int. J. Comput. Cognition, 8(3)(2010), 85-89.
[12] Rao, G.C. and Mihret Alamneh, Po Almost Distributive Lattices, (To appear)
[13] U.M. Swamy and G.C. Rao. Almost Distributive Lattices, J. Aust. Math. Soc. (Series A), 31(1981), 77-91.
[14] G. Szasz. Derivations of lattices, Acta Sci. Math.(Szeged), 37(1-2)(1975), 149-154.
[15] X.L.Xin, T. Y. Li and J. H. Lu. On derivations of lattices, Information Science, 178(2008), 307-316.
[16] X.L.Xin, The fixed set of derivations in lattices, Fixed Point Theory and Appl., 2012: 218.
doi:10.1186/1687-1812-2012-218
[17] H. Yazarli and M. A. Ozlurk., Permuting Tri-f-derivations in lattices, Commun. Korean Math. Soc., 26(1)(2011), 13-21.
[2] H.E.Bell and L.C.Kappe. Ring in which derivations satisfy certain algebraic conditions, Acta Math. Hung., 53(3-4)(1989), 339-346.
[3] Y. Ceven and M. A. Ozturk. On f-derivations of lattice, Bull. Korean Math. Soc., 45(4)(2008), 701-707.
[4] Y. Ceven. Symmetric Bi-derivations of lattice, Quaestiones Mathematicae, 32(2)(2009), 241-245.
[5] K.Kaya. Prime rings with a derivations, Bull. Mater. Sci. Eng,16(1987), 63-71.
[6] K. H. Kim. Symmetric Bi-f-derivations in lattices, Int. J. Math. Archive, 3(10)(2012), 3676-3683.
[7] M. Asci and S. Ceran. Generalized (f,g)-Derivations of Lattices, Math. Sci. Appl., E-notes, 1(2)(2013), 56-62.
[8] M. A. ztrk, H. Yazarli and K. H. Kim. Permuting tri-derivations in lattices, Quaestiones Mathematcae, 32(3)(2009), 415-425.
[9] E. Posner. Derivations in prime rings, Proc. Amer. Math. Soc., 8(6)(1957), 1093-1100.
[10] Rao, G.C. Almost Distributive Lattices. Doctoral Thesis, Dept. of Mathematics, Andhra University, Visakhapatnam. 1980
[11] Rao, G.C. B. Assaye and M. V. Ratna Mani. Heyting Almost Distributive Lattices, Int. J. Comput. Cognition, 8(3)(2010), 85-89.
[12] Rao, G.C. and Mihret Alamneh, Po Almost Distributive Lattices, (To appear)
[13] U.M. Swamy and G.C. Rao. Almost Distributive Lattices, J. Aust. Math. Soc. (Series A), 31(1981), 77-91.
[14] G. Szasz. Derivations of lattices, Acta Sci. Math.(Szeged), 37(1-2)(1975), 149-154.
[15] X.L.Xin, T. Y. Li and J. H. Lu. On derivations of lattices, Information Science, 178(2008), 307-316.
[16] X.L.Xin, The fixed set of derivations in lattices, Fixed Point Theory and Appl., 2012: 218.
doi:10.1186/1687-1812-2012-218
[17] H. Yazarli and M. A. Ozlurk., Permuting Tri-f-derivations in lattices, Commun. Korean Math. Soc., 26(1)(2011), 13-21.
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2016-12-26
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