Zhu Tian-min
Abstract
This paper studies the multiplicative band semirings whose additive reducts are semilattice. Through studying Green -D relation, it is proved that if S ∈S+ l, S is multiplicative band semirings if and only if S is distributive lattice. Thus the theorem about structure of distributive lattice is obtained.
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This paper studies the multiplicative band semirings whose additive reducts are semilattice. Through studying Green -D relation, it is proved that if S ∈S+ l, S is multiplicative band semirings if and only if S is distributive lattice. Thus the theorem about structure of distributive lattice is obtained.
Key concepts: Semilattice, Distributive property, Distributive lattice, Multiplicative function, Congruence lattice problem, Lattice (music), Mathematics, Pure mathematics