Introduced by Ch.S. Pierce and E. Schröder and independently by R. Dedekind, and afterwards developed by G. Birkhoff, V. Glivenko, K. Menger, J. von Neumann, O. Ore and others, Lattice Theory is a highly topical field, with many applications in mathematics.
Distributive lattices represent the starting point in Lattice Theory; their study is required by more and more frequent situations when distributivity is imposed by applications.
A weaker condition of distributivity is the modularity, introduced by R. Dedekind.
Modularity and distributivity are characterized in this chaper, using hyperstructures, particularly join spaces.
KeywordsDistributive Lattice Direct Limit Inverse Limit Modular Lattice Direct Family
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