Lattice implication ordered semigroups |
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| Authors: | Xiaodong Pan Yang Xu |
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| Affiliation: | a Department of Mathematics, Southwest Jiaotong University, Chengdu 610031, Sichuan, PR China
b Intelligent Control Development Center, Southwest Jiaotong University, Chengdu 610031, Sichuan, PR China |
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| Abstract: | From the viewpoint of semantics, lattice implication algebras provide a basis to establish lattice-valued logic with truth value in a relatively general lattice. In this paper, we first introduce two notions of lattice implication n-ordered semigroup and lattice implication p-ordered semigroup, which induced by lattice implication algebras. Secondly, we study some of their basic properties and prove that a lattice implication n-ordered semigroup is a residuated semigroup, and a lattice implication p-ordered semigroup is an arithmetic lattice ordered semigroup. We also define the homomorphism mapping between lattice implication n-ordered semigroups. Finally, we discuss some properties of filters and sl ideals in lattice implication n-ordered semigroups and lattice implication p-ordered semigroups. |
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| Keywords: | Lattice ordered semigroup Implication semigroup Lattice implication algebra Filter sl Ideal |
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