2007•Journal of Qingdao University of Science and TechnologyRequires access

Distributive Lattice Characterized by a Class of Idempotent Semirings

Zhu Tian-min

Abstract

A class of idempotent semirings which can be showed distributive lattice,i.e.,multiplicative band semirings which additive reducts are semilattice are studied in this paper.Some properties of multiplicative bond semirings are obtained by Green-D relation.We also proved S∈ +S,S is multiplicative band semirings if and only if S is distributive lattice.The characterization for structure of distributive lattice is obtained.

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Key concepts: Semilattice, Distributive property, Multiplicative function, Idempotence, Distributive lattice, Congruence lattice problem, Mathematics, Lattice (music)