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2010•Shuxue de shijian yu renshiRequires access

Another Two Laws for Distributive Lattices and Modular Lattices

Mu Ren, MA Zhan-xin, Zhang Run-long

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Abstract

For the problems of the definitions of distributive lattices and modular lattices, we found two laws are the least law for distributive lattices and modular lattices,and we proved Sholander's basis is the shortest and least variables identities for distributive lattices. At last,according to the definition of distributive lattices and modular lattices,We provided another new two laws and three laws for distributive lattice and modular lattices.

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What this paper is about

For the problems of the definitions of distributive lattices and modular lattices, we found two laws are the least law for distributive lattices and modular lattices,and we proved Sholander's basis is the shortest and least variables identities for distributive lattices. At last,according to the definition of distributive lattices and modular lattices,We provided another new two laws and three laws for distributive lattice and modular lattices.

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Available abstract

For the problems of the definitions of distributive lattices and modular lattices, we found two laws are the least law for distributive lattices and modular lattices,and we proved Sholander's basis is the shortest and least variables identities for distributive lattices. At last,according to the definition of distributive lattices and modular lattices,We provided another new two laws and three laws for distributive lattice and modular lattices.

Key concepts: Distributive property, Modular design, Distributive lattice, Lattice (music), Congruence lattice problem, Pure mathematics, Mathematics, Map of lattices

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