First, we reviewed the definitions of lattice implication algebras, lattice implication subalgebras, and LI-ideals, and provided an equivalent definition of LI-ideal. Then we investigated some properties of lattice im...First, we reviewed the definitions of lattice implication algebras, lattice implication subalgebras, and LI-ideals, and provided an equivalent definition of LI-ideal. Then we investigated some properties of lattice implication subalgebra and U-ideal, and found the least lattice implication subalgebra. Finally, the relation between lattice implication subalgebra and LI-ideal is presented. It is proved that no LI-ideals are non-trivial lattice implication subalgebras.展开更多
In this paper, the concept of α-subsets is introduced in a lattice implication algebra and some properties are discussed. Then we prove that an α-subset is a lattice ideal of L. In the end, we discuss the properties...In this paper, the concept of α-subsets is introduced in a lattice implication algebra and some properties are discussed. Then we prove that an α-subset is a lattice ideal of L. In the end, we discuss the properties of annihilator.展开更多
基金The National Natural Science Foundationof China (No.60875034)the Specialized Research Fundfor the Doctoral Program of Higher Education of China (No.20060613007)
文摘First, we reviewed the definitions of lattice implication algebras, lattice implication subalgebras, and LI-ideals, and provided an equivalent definition of LI-ideal. Then we investigated some properties of lattice implication subalgebra and U-ideal, and found the least lattice implication subalgebra. Finally, the relation between lattice implication subalgebra and LI-ideal is presented. It is proved that no LI-ideals are non-trivial lattice implication subalgebras.
基金Supported by the National Natural Science Foundations of P.R.China(No.60474022)
文摘In this paper, the concept of α-subsets is introduced in a lattice implication algebra and some properties are discussed. Then we prove that an α-subset is a lattice ideal of L. In the end, we discuss the properties of annihilator.
