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- Title
On Derivations of State Residuated Lattices.
- Authors
Kuanyun Zhu; Jingru Wang; Yongwei Yang
- Abstract
In this paper, we intoduce the notion of derivations of state residuated lattices (L,Τ) and discuss some properties of them. We study the related properties of strong derivations and regular derivations of state residuated lattices (L,Τ). Moreover, we propose the notion of (strong) state-morphism residuated lattices and discuss some properties of them. Also, the principal ideal derivation is given and the adjoint of principal ideal derivation is obtained by a Galois connection, and we prove that the set of all principal ideal derivations on state-morphism residuated lattice (L,Τ) can form a bounded distributive lattice. Further, a special kind of set Ima(d,Τ)(L) of a derivation on state residuated lattices (L,Τ) is introduced and we get that Ima(d,Τ)(L) is a lattice ideal of L, when derivation d is a regular ideal derivation. In particular, if L is a linearly ordered residuated lattice, then Ima(d,Τ)(L) is a prime lattice ideal of L. Finally, by using the set Ima(d,Τ)(L) of principal ideal derivations, we give a characterization of a Heyting algebra.
- Subjects
DISTRIBUTIVE lattices; RESIDUATED lattices; HEYTING algebras; PRIME ideals
- Publication
IAENG International Journal of Applied Mathematics, 2020, Vol 50, Issue 4, p751
- ISSN
1992-9978
- Publication type
Article